Week 8 · Chapter

Chapter 8 — Midterm Review & Exam

Critical Thinking Free sample edition

The module's primary reading · ~30–40 minutes · Objective 1 (identify claims and arguments in everyday and academic passages, distinguishing arguments from explanations, reports, and unsupported assertions, and locate premises and conclusions with and without indicator words), Objective 2 (analyze an argument by putting it in standard form, supplying unstated premises under the principle of charity, and mapping how its premises, objections, and replies connect, described in words), Objective 3 (evaluate deductive reasoning: distinguish deductive from inductive arguments, apply validity, soundness, strength, and cogency, use the counterexample method, recognize the valid conditional forms and the two formal fallacies, state necessary and sufficient conditions, and test categorical syllogisms with Venn diagrams), Objective 4 (explain how language shapes reasoning through definitions, vagueness, ambiguity, equivocation, and loaded wording, and identify the common informal fallacies of relevance and presumption while distinguishing a fallacy from a false premise and from legitimate criticism) · Read it early this week, before the practice set and the discussion and well before the midterm.

In plain language

This week you look back at the first seven weeks and see how they fit together. Each topic so far asks for one test (a question you run on a passage) or one distinction (two ideas that sound alike but must be kept apart). You will sort every week by that test, so you know which one to reach for. You will also learn one small new family of mistakes, the fallacies of presumption (arguments that quietly assume the very thing they should support). Then you sit the midterm, which checks that you can run each test yourself.

Why you already care about this

It is the week before a midterm. You have 7 weeks of notes open, 6 argument forms, 6 syllogisms, and 12 fallacy passages, and every page looks equally important. A classmate in your study group says, "Either we reread everything or we fail." Another asks, "Have you stopped leaving your reviewing to the last night?" Nobody has answered the real question yet: where do you start?

Here is one way in. Every topic in the first half of the course asks for one test or one distinction. Week 3 asks "valid or sound?" Week 4 asks "converse or contrapositive?" Week 7 asks "fallacy or false premise?" If you can say which test a passage calls for, you have done most of the work, because each test then runs the same way it ran the first time.

Notice the two lines from the study group, too. One offers you two options as if there were no third. The other asks a question you cannot answer yes or no without admitting something you may not have done. Those are this week's new material, and by the end of the chapter you will be able to name both.

By the end of this chapter you will be able to:

tell an argument from an explanation and put an argument in standard form with its supplied premise marked;
say whether an argument is valid, sound, strong, or cogent, and why the running question can be no better than cogent;
tell a conditional from its converse and its contrapositive, and state which condition is necessary and which is sufficient;
read a Venn verdict from the shaded and marked regions;
tell vagueness from ambiguity, and a fallacy from a false premise;
identify the false dilemma, begging the question, and the loaded question, and expose each by writing its hidden assumption as a supplied premise.

Carry this line with you: name the test first; then run it, not the other way round.

Where we are

Already covered: Weeks 1 to 7 built the whole first half of the course: finding arguments, standard form and maps, validity and strength, the conditional forms, categorical reasoning, language and meaning, and the fallacies of relevance.
This week: a review of all seven weeks, one test or distinction per topic, plus one new family of fallacies, the fallacies of presumption, and the midterm.
How they connect: the fallacies of presumption are exposed with Week 2's supplied premise and judged with Week 7's line between a fallacy and a false premise.
Where we're going next: Week 9 opens the second half of the course, Inductive Generalization and Analogy, where the tests turn from the passage on the page to the evidence in the world.

Week 1 taught you to find an argument and tell it from an explanation. Week 2 taught you standard form, the supplied premise, and the argument map. Week 3 taught you validity, soundness, strength, cogency, and the counterexample method. Week 4 taught you the conditional forms and the two formal fallacies. Week 5 taught you the Venn test. Week 6 taught you how words can shift meaning or carry a verdict. Week 7 taught you the fallacies of relevance. Every section below reuses an example you have already met; the only new passages are the three fallacies of presumption.

1. Find it and write it out: argument versus explanation, and standard form

Picture a text from a teammate on a rainy afternoon. "The game was canceled because the field flooded." Everyone already knows the game is off, so the teammate is telling you why. Now picture a different text: "The game will be canceled, because the field is flooding." Nobody knows yet, so the teammate is giving you a reason to believe it.

That is Week 1's distinction:

An argument gives reasons to believe a claim that is in question.
An explanation gives reasons why something already accepted is so.

The test is one question about the audience: is the claim being supported in doubt for them? The word "because" appears in both texts, so it cannot settle the matter by itself.

Week 2 then taught you to write an argument out. In standard form, each premise sits on its own numbered line, P1, P2, P3; a line reading "So," comes next; and the conclusion sits on its own line, marked C. A premise you add because the arguer left it unsaid is marked "(supplied)".

Worked example — the running question in standard form (illustrative). Here is the campus-newsletter argument you have tested since Week 1.

P1: During finals week many students need a quiet, safe place to study late at night.

P2: The library is the only quiet, safe, well-lit study space on campus large enough to meet that need.

P3 (supplied): The campus should provide study space students need during finals when it can do so at modest cost.

P4: Keeping the library open overnight for the five nights of finals week costs about 1,600 dollars in staff wages.

So,

C: The campus library should stay open around the clock during finals week.

Count the stated premises. P1, P2, and P4 come from the newsletter: 3 stated premises.
Count the supplied premise. P3 is yours: 1 supplied premise.
Count the lines. 3 + 1 = 4 premises, and 4 premises + 1 conclusion = 5 lines.
Check the charity. P3 is the weakest premise that closes the gap between the need and the conclusion. It asks the campus to act only when the cost is modest.

In words: the newsletter argues for a proposal still in question, and standard form shows 4 premises, one of them supplied, leading to one conclusion.

Misconception check — "because" always marks a premise. Students often treat every "because" as the start of a reason in an argument. That is tempting, because "because" is on the list of premise indicators. But the canceled-game text uses "because" to explain a result everyone accepts. Ask whether the claim is in doubt for the audience before you call a passage an argument.

Memory hook: in doubt, it argues; accepted, it explains.

2. Judge the link: valid versus sound, strong versus cogent

A friend tells you, "Every bus on this route stops at the library, and this is a bus on this route, so it stops at the library." If both premises are true, the conclusion cannot miss. Another friend says, "The app says rain is likely, so I'm bringing an umbrella." The reason makes the conclusion likely, not certain. Week 3 gave those two promises their names and their tests.

An argument is valid when it is impossible for all its premises to be true and its conclusion false. It is sound when it is valid and every premise is true.
An inductive argument is strong when its premises, if true, make its conclusion likely, and strength comes in degrees. It is cogent when it is strong and every premise is true.

Valid is a fact about the link. Sound adds a fact about the premises. The same split holds for strong and cogent.

Worked example — the running question's two links. Test each support link on the map.

The first link. P1, P2, and P3 lead to C validly once the cost is granted to be modest. If the cost is modest, the three premises leave no room for C to be false.
The figure behind P4. 2 staff × 8 hours × 5 nights × 20 dollars an hour = 1,600 dollars. Step by step: 2 × 8 = 16 staff hours a night; 16 × 5 = 80 staff hours; 80 × 20 = 1,600 dollars.
The second link. Can P4 be true while "the cost is modest" is false? It can. A campus that has spent its whole study-space budget might not call 1,600 dollars modest. So P4 makes "modest" likely but cannot guarantee it, and that link is inductive.
The tally. 1 deductive link + 1 inductive link = 2 support links.

In words: because one link is inductive, the argument as a whole can be no better than cogent, and the places to look hardest are the inductive step and the truth of P3.

Misconception check — valid means true. Students often hear "valid" and think "correct." That is tempting, because in everyday speech a valid remark is a good one. But a valid argument can have a false conclusion when a premise is false, and an invalid argument can have a true conclusion it fails to support. Valid answers one question only: could the premises be true and the conclusion false?

A second trap sits beside the first: cogent read as meaning valid. A cogent argument is a strong inductive one with true premises. It makes its conclusion likely, and even a cogent argument can have a false conclusion.

Memory hook: valid is the link; sound is the link plus the facts.

3. Read the conditional: converse versus contrapositive, necessary versus sufficient

A sign by the student-services desk says you can register for a course only if you passed the prerequisite. A classmate who passed the prerequisite says, "Great, so I'm registered." Then the course turns out to be full. The sign was about what you need, not about what is enough. Week 4 taught you to read that kind of sentence exactly.

A conditional is a claim of the form "if P, then Q", where the sentence letters P and Q stand for whole claims. It is false in exactly one situation: P true and Q false. Turn it around three ways and you get:

the converse, "if Q, then P", which is not equivalent to the original;
the inverse, "if not P, then not Q", which is not equivalent either;
the contrapositive, "if not Q, then not P", which is equivalent: it is true or false together with the original in every case.

In "if P, then Q", P is a sufficient condition for Q, and Q is a necessary condition for P.

Worked example — the soccer field and the registration sign (illustrative). Turn one conditional around, refute the two formal fallacies, and read one "only if" sign.

The conditional. "If it rained overnight, the soccer field is wet."
The contrapositive. "If the soccer field is not wet, it did not rain overnight." This one is equivalent.
The converse. "If the soccer field is wet, it rained overnight." This one is not equivalent.
The counterexample. The sprinklers ran overnight and it did not rain. Then the premises of affirming the consequent ("the field is wet, so it rained") are both true, and its conclusion is false. On the same morning the premises of denying the antecedent ("it did not rain, so the field is not wet") are both true, and its conclusion is false.
The tally of forms. That leaves 4 valid forms + 2 invalid forms = 6 forms in the set.
The truth-table check. 2 sentence letters, each true or false, give 2 × 2 = 4 rows, and the conditional is false in 1 row: P true and Q false.
The registration sign. "You can register for the course only if you passed the prerequisite" means "if you can register, you passed the prerequisite." Passing is necessary for registering, but it is not sufficient: you also need an open seat.

In words: only the contrapositive says the same thing as the original, one sprinkler morning refutes both formal fallacies, and the prerequisite is something you need without being enough.

Misconception check — the converse says the same thing. Students often flip a conditional and think nothing changed. That is tempting, because the same two claims appear in both. But "if the field is wet, it rained" fails on the sprinkler morning, while the original holds. When you turn a conditional around, swap and deny both parts, or you have changed its meaning.

A second swapped pair lives here too: a necessary condition read as a sufficient one. The classmate who passed the prerequisite made exactly that slip.

Memory hook: swap and deny both, or you changed the claim.

4. Check the regions: the Venn verdict

A dog-park flyer says every poodle there is a dog and every beagle there is a dog. Someone concludes that every poodle there must be a beagle. You can feel that something is off, but Week 5 gave you a picture test that shows exactly what.

A Venn diagram tests a categorical syllogism with one circle for each term. You shade every region the premises say is empty, place an X wherever a premise says at least one thing exists, and then check whether the conclusion's region is already settled. Shading means empty; an X means at least one thing. Neither tells you how many things a region holds.

Worked example — the poodles and the beagles (illustrative). "All poodles are dogs. All beagles are dogs. So all poodles are beagles."

Draw three circles. One each for poodles, beagles, and dogs.
Shade for the first premise. Shade the part of the poodle circle outside the dog circle.
Shade for the second premise. Shade the part of the beagle circle outside the dog circle.
Check the conclusion's region. "All poodles are beagles" needs the part of the poodle circle outside the beagle circle to be empty. The region of poodles that are not beagles, inside the dog circle, is left unshaded.
The tally of the set. The categorical-syllogism set holds 3 valid syllogisms + 3 invalid syllogisms = 6.

In words: the premises leave open a region that could hold a poodle that is not a beagle, so the syllogism is invalid, even though both premises are true.

Misconception check — two premises that share a term are enough. Students often see "dogs" in both premises and assume the premises must connect the other two groups. That is tempting, because the sentences sound linked. But sharing a term does not force the conclusion's region to be shaded. The diagram, not the sound of the sentences, gives the verdict.

Another slip to watch: reading a Venn diagram as a count. An X in a region says at least one thing is there, not how many.

Memory hook: shade first, then the X, then look at the conclusion's region.

5. Watch the words and the link: vagueness versus ambiguity, fallacy versus false premise

A driver reads a sign by a curb: "Fine for parking here." The driver parks, sure that no ticket is coming. The ticket comes anyway. Week 6 and Week 7 together explain what went wrong, and they hand you two more distinctions.

Week 6's distinction:

A vague term has borderline cases, where it is unclear whether the word applies, such as "late at night".
An ambiguous term has two or more distinct meanings that both fit its context, such as "fine" read as a penalty or as "all right".

Equivocation is the fallacy of letting one word shift meaning between steps, so the argument only seems to connect.

Week 7's distinction:

A fallacy is a flaw in the reasoning that connects the premises to the conclusion.
A false premise is a flaw in content, a premise that is not true.

Worked example — the parking sign, the treasurer, and P2 (illustrative). Sort each failure as a word problem, a reasoning problem, or a fact problem.

The parking sign. "The sign says 'Fine for parking here.' Since it is fine to park here, I won't get a ticket." On the sign, "fine" means a penalty; in the conclusion, it means "all right". "Fine" is ambiguous, so the passage commits equivocation.
A vague word for contrast. "Late at night" has borderline cases, but it has no second meaning. Vagueness alone causes no equivocation.
The treasurer. "We can ignore the treasurer's budget proposal; she failed a math class in high school." Even if the grade story is true, it would not bear on whether the budget adds up. That is a flaw in the reasoning, so the passage commits the attack on the person (ad hominem).
A false premise for contrast. Suppose the running question's P2 turned out false, because the campus had another quiet, safe, well-lit space large enough. Then the argument would have a false premise, not a fallacy. Its reasoning would still hold together; its facts would fail.
The tally of keys so far. 3 Week 6 passages + 9 Week 7 passages = 12 fallacy passages keyed through Week 7.

In words: the parking sign fails because one word changes meaning, the treasurer passage fails because its premise does not bear on the conclusion, and a false P2 would fail on the facts instead of the reasoning.

Misconception check — a false premise is a fallacy. Students often call any argument with a false claim "a fallacy." That is tempting, because everyday speech uses "fallacy" for any mistaken belief. But in this course a fallacy is a flaw in the reasoning. Check the link and the facts separately, and name the one that failed.

A caveat on vagueness: a vague word is not a useless one. Most useful words are vague at the edges, and a precising definition, like the 1,600 dollars that made "modest cost" precise in Week 6, fixes vagueness when an argument needs it.

Memory hook: one word, two meanings, is ambiguity; one word, fuzzy edges, is vagueness.

6. Find the hidden assumption: the fallacies of presumption

Here is the new material. At a campus forum, a speaker says, "Either we raise student parking fees or the library closes on weekends." The room splits into two camps, fees or closures. Nobody asks whether those are the only two choices on the table. The argument never said they were; it presumed it.

A fallacy of presumption is a fallacy in which an argument quietly assumes, without support, the very thing it should be supporting. This week covers three of them. Each name has a second name in common use, and either is correct.

A false dilemma (false dichotomy) presents two options as the only ones when others exist, so rejecting one seems to force the other.
Begging the question (circular reasoning) assumes in a premise what the conclusion is meant to show, so the argument restates its conclusion instead of giving an independent reason.
A loaded question (complex question) builds a disputed claim into the question, so any direct yes or no answer concedes the claim.

The cure for all three is a move you learned in Week 2. Write the hidden assumption out as a supplied premise, mark it "(supplied)", and ask what supports it.

Worked example — the three Week 8 passages (illustrative). Run the hidden-assumption check on each passage from the course's fallacy set.

The parking fees. "Either we raise student parking fees or the library closes on weekends." Written out and marked, the hidden premise is "(supplied) These are the only two options." Nothing supports it, and other options exist, such as shorter weekend hours or savings elsewhere in the budget. The passage commits the false dilemma (false dichotomy).
The class schedule. "The new class schedule is the best schedule because no other schedule is better." The premise, "no other schedule is better", says what the conclusion says in other words. It assumes what it should show, so the passage commits begging the question (circular reasoning).
The phone. "Have you stopped wasting time on your phone during lectures?" The question builds in the disputed claim "you have been wasting time on your phone during lectures." A yes admits you used to; a no admits you still do. The passage commits the loaded question (complex question).
The tally. 1 false dilemma + 1 begging the question + 1 loaded question = 3 Week 8 passages. 12 + 3 = 15 passages keyed through Week 8, and 20 − 15 = 5 passages still to come in later weeks.

In words: each passage leans on an assumption it never supports, the only-two-options claim, the conclusion itself, or the built-in accusation, so each commits one fallacy of presumption.

Notice something odd about the class-schedule passage. In standard form it reads "P1: No other schedule is better than the new class schedule. So, C: The new class schedule is the best schedule." That is valid: if the premise were true, the conclusion could not be false. The trouble is that the premise is the conclusion in other words. Anyone who doubts the conclusion has no reason to accept the premise, so the argument gives them nothing. Validity is not the whole story.

Misconception check — begging the question means raising the question. Students often hear "this begs the question" used to mean "this makes me want to ask." That is tempting, because the everyday phrase is common. But in this course, begging the question is the fallacy of assuming what the conclusion is meant to show. If you mean "it raises the question", say "it raises the question."

An honesty note: these three sit close to Week 7's line between a fallacy and a false premise. The supplied premise in a false dilemma is often false. What makes the passage a fallacy of presumption is that the argument hides that premise and treats it as settled, so the audience never gets the chance to check it.

Memory hook: write the hidden assumption down, then ask what holds it up.

7. Name the test first: the neighbors, and the midterm

A friend at a coffee shop says, "A claim is either true or false, so this one is one or the other." That is an either-or, but nobody would call it a false dilemma. Every new fallacy in this course has had a non-fallacious neighbor, and the presumption fallacies do too. Spotting the neighbor keeps you from flagging good reasoning.

The real two-option choice. Two options are fine when they really are the only two. A claim is either true or false, with no third choice, and each sentence letter in a truth table is either true or false.
The raised question. Saying "that raises the question of cost" is not begging the question. It asks for more reasons; it does not assume the conclusion.
The challenged question. A loaded question is challenged, not answered. "I don't accept that I was wasting time; ask me how I use my phone in lectures" separates the hidden claim and puts it up for evidence.

Worked example — name the test first (illustrative). Each passage below is one you have met. Say which test it calls for before you run it.

"If the soccer field is wet, it rained overnight; the field is wet; so it rained." An "if" sentence calls for the conditional test. The form affirms the consequent, and the sprinkler morning refutes it.
"All poodles are dogs. All beagles are dogs. So all poodles are beagles." "All" sentences about groups call for the Venn test. The region of poodles that are not beagles stays unshaded, so the syllogism is invalid.
"Most people in the group chat think the new attendance rule is unfair, so it must be unfair." A reason that may not bear on the conclusion calls for the relevance test. A head count replaces reasons, so the passage commits the appeal to popularity (ad populum).
"Either we raise student parking fees or the library closes on weekends." An either-or offered as the whole menu calls for the hidden-assumption check. The only-two-options premise is unsupported, so the passage commits the false dilemma.

In words: once you name the test, each verdict follows the same steps it followed the first time, and the passage itself tells you which test it needs.

That is also how to meet the midterm. It covers Objectives 1 to 4 as taught in Weeks 1 to 7; this week's three fallacies of presumption are practiced in the discussion and the practice set, not on the midterm. You take it on your own, with no AI help, because it confirms that you personally can identify an argument, test its form, and name a fallacy. For each item, name the test first, then run it, then say the verdict in one plain sentence.

Misconception check — any argument with two options is a false dilemma. Students often flag every either-or sentence once they learn this fallacy. That is tempting, because the false dilemma always comes in two options. But two options are fine when they really are the only two. The test is not "are there two options?" It is "does anything support the claim that these are the only two?"

A last limitation: the fallacy catalog is a classroom tool, not a machine. A borderline passage, where a third option is possible but far-fetched, is for discussion, not for a quiz.

Memory hook: two options are fine when they really are the only two.

Key terms

argument — A set of claims in which one or more, the premises, are offered as reasons to accept another, the conclusion. (first used: 1. Find it and write it out: argument versus explanation, and standard form)
explanation — A set of claims that gives reasons why something already accepted is so, rather than reasons to believe something still in question. (first used: 1. Find it and write it out: argument versus explanation, and standard form)
valid — Said of an argument when it is impossible for all its premises to be true and its conclusion false; validity depends on the argument's form, not on whether the premises are in fact true. (first used: 2. Judge the link: valid versus sound, strong versus cogent)
sound — Said of an argument that is valid and has every premise true; a sound argument's conclusion must be true. (first used: 2. Judge the link: valid versus sound, strong versus cogent)
strong — Said of an inductive argument whose premises, if true, would make its conclusion likely; strength comes in degrees, and an argument that falls short is weak. (first used: 2. Judge the link: valid versus sound, strong versus cogent)
cogent — Said of a strong inductive argument whose premises are all true; even a cogent argument can have a false conclusion. (first used: 2. Judge the link: valid versus sound, strong versus cogent)
contrapositive — The conditional made by swapping and denying both parts of if P, then Q to get if not Q, then not P; it is always true or false together with the original. (first used: 3. Read the conditional: converse versus contrapositive, necessary versus sufficient)
necessary condition — A condition that must hold for another to hold, though it may not be enough on its own; in if P, then Q, the then-part Q is necessary for P. (first used: 3. Read the conditional: converse versus contrapositive, necessary versus sufficient)
Venn diagram — A drawing of overlapping circles, one for each term, used to test a categorical syllogism: a shaded region is empty, and an X sits in a region that holds at least one thing. (first used: 4. Check the regions: the Venn verdict)
ambiguous term — A word or phrase with two or more distinct meanings that both fit its context, such as fine read as a penalty or as all right. (first used: 5. Watch the words and the link: vagueness versus ambiguity, fallacy versus false premise)
false premise — A premise that is not true, a flaw in an argument's content rather than in its reasoning; an argument can have a false premise and still be valid. (first used: 5. Watch the words and the link: vagueness versus ambiguity, fallacy versus false premise)
fallacy of presumption — A fallacy in which an argument quietly assumes, without support, the very thing it should be supporting, so the conclusion rests on an assumption the audience was never asked to accept. (first used: 6. Find the hidden assumption: the fallacies of presumption)
false dilemma (false dichotomy) — The fallacy of presenting two options as the only ones when others exist, so that rejecting one seems to force the other. (first used: 6. Find the hidden assumption: the fallacies of presumption)
begging the question (circular reasoning) — The fallacy of assuming in a premise what the conclusion is meant to show, so the argument restates its conclusion in other words instead of giving an independent reason for it. (first used: 6. Find the hidden assumption: the fallacies of presumption)
loaded question (complex question) — A question that builds a disputed claim into its wording, so that any direct yes or no answer concedes the claim; the fair response is to challenge the hidden claim instead of answering. (first used: 6. Find the hidden assumption: the fallacies of presumption)

Summary

An argument supports a claim in doubt; an explanation accounts for one already accepted.
Standard form numbers each premise, marks a supplied one, and puts C last.
Valid is about the link; sound adds true premises. Strong and cogent split the same way.
Only the contrapositive is equivalent to a conditional; the converse is not.
In "if P, then Q", P is sufficient and Q is necessary.
A Venn verdict comes from the shaded and marked regions, never from how the sentences sound.
Vagueness is fuzzy edges; ambiguity is two meanings.
A fallacy breaks the reasoning; a false premise breaks the facts.
The false dilemma, begging the question, and the loaded question each hide an unsupported assumption.
Write the hidden assumption as a supplied premise, then ask what supports it.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A running coach tells a new runner (illustrative): "Either you run every single morning or you will never finish the race." Name the fallacy, write the hidden assumption as a supplied premise, and give one option the coach left out.
A product page says (illustrative): "This blender is the most reliable on the market because it is more dependable than every other blender." Name the fallacy. Is the argument valid? Does it give a doubter any reason?
A team lead asks a new hire in front of the group (illustrative): "Why do you keep ignoring the team's deadlines?" Name the fallacy and write a reply that challenges the question instead of answering it.
A kitchen sign reads (illustrative): "If the oven light is on, the oven is heating." Write the contrapositive and the converse, say which one is equivalent, and say which part is necessary for the other.

Answers (worked reasoning — read after attempting)

The false dilemma (false dichotomy). Written out and marked, the hidden assumption is "(supplied) Running every single morning and never finishing are the only two options." Nothing supports it. A runner could train four days a week with rest days and still finish, so other options exist.
Begging the question (circular reasoning). "More dependable than every other blender" says the same thing as "the most reliable" in other words. The argument is valid, because if the premise were true the conclusion could not be false. But a doubter has no more reason to accept the premise than the conclusion, so the argument gives them nothing.
The loaded question (complex question). It builds in the disputed claim "you have been ignoring the team's deadlines." A direct answer about why concedes that claim. A challenge separates it: "I don't accept that I've been ignoring deadlines; can we look at which ones you mean?"
The contrapositive is "If the oven is not heating, the oven light is not on", and it is equivalent to the sign. The converse is "If the oven is heating, the oven light is on", and it is not equivalent: the light could be broken while the oven heats. The oven heating is necessary for the light being on, and the light being on is sufficient for the oven heating.

Next up in this module: the lecture, the slide deck, the Readings & Resources page, the practice set, the discussion, and the midterm. Next week, in Inductive Generalization and Analogy, the sampling test asks whether a sample can speak for its whole population.

Built with The Course Maker · samples.thecoursemaker.com