Valid and Invalid Deductions ACET Reviewer: Lesson and Practice

TEACHER ABI ACET LOGICAL REASONING

Valid and Invalid Deductions

Judge an argument by its structure, not by whether its conclusion sounds believable.

One focused competency6 worked examples27 original questionsEasy to ACET-level

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Valid and Invalid Deductions

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Valid means the conclusion cannot fail if the premises are true

If the sensor detects smoke, the alarm sounds.The sensor detected smoke.Therefore, the alarm sounded.

Valid. The trigger occurred, so the promised result follows.

Now compare:

If the sensor detects smoke, the alarm sounds.The alarm sounded.Therefore, the sensor detected smoke.

Invalid. The alarm might have sounded during a test or for another reason.

Validity is structural. A true conclusion can still come from invalid reasoning.

DO IT FAST

Use FORM → LINK → COUNTEREXAMPLE

1. FORM: Reduce the argument to a familiar pattern.
2. LINK: Check that every needed step is supplied in the correct direction.
3. COUNTEREXAMPLE: Try to make all premises true and the conclusion false. If you can, the deduction is invalid.

P → Q; P; therefore Q = valid
P → Q; not Q; therefore not P = valid
P → Q; Q; therefore P = invalid

WORKED EXAMPLES

Six forms you must recognize

1. Modus ponens

If P, then Q. P.

Therefore Q. Valid.

2. Modus tollens

If P, then Q. Not Q.

Therefore not P. Valid.

3. Affirming the consequent

If P, then Q. Q.

Therefore P is invalid. Q may have another cause.

4. Denying the antecedent

If P, then Q. Not P.

Therefore not Q is invalid. Q may still occur another way.

5. Disjunctive syllogism

P or Q. Not P.

Therefore Q. Valid.

6. Hypothetical chain

If P, then Q. If Q, then R. P.

Therefore R. Valid.

GUIDED TRY

Test the structure

If a parcel is fragile, it receives special handling.Parcel T received special handling.Therefore, T is fragile.

1. The rule runs from fragile to special handling.
2. The argument starts from special handling and moves backward.
3. Can a non-fragile parcel receive special handling for another reason?

Invalid. A refrigerated or valuable parcel might also receive special handling. The premises can be true while the conclusion is false.

COMMON TRAPS

Do not reward a believable conclusion

True conclusion = valid: Truth and validity are different questions.

Running an arrow backward: Q does not establish P.

Removing the trigger: Not P does not establish not Q.

Skipping a premise: Every link in a chain must be supported.

Inventing overlap: Shared traits do not force shared members.

Using outside facts: Test only the stated premises.

FIVE-FORM SKILL CHECK

Do you need Foundations or Core Practice?

CHOOSE YOUR PRACTICE

Build the skill in stages

Foundations

Recognize the four basic conditional forms.

Core

Disjunctions, category links, and chains.

ACET Transfer

Dense arguments and counterexamples.

FRESH MASTERY CHECK

Can you decide without the scaffolding?

Score 5/5 to verify this competency. If not, a fresh set loads.

QUICK ANSWERS

Valid and Invalid Deductions FAQ

Can a valid argument have a false conclusion?

If its premises are actually false, yes. Validity says only that true premises would force the conclusion.

Can an invalid argument have a true conclusion?

Yes. The conclusion may happen to be true even though the premises do not prove it.

What is the fastest validity test?

Try to build a case where every premise is true but the conclusion is false.

Why is affirming the consequent invalid?

The result may have more than one possible cause, so observing the result does not identify the stated trigger.

Why is modus tollens valid?

If P always requires Q, the absence of Q rules out P.

Do I need to memorize the Latin names?

The patterns matter more than the labels. Learn the structure first.

RELATED LOGICAL REASONING COMPETENCIES

Continue the reasoning pathway

Statements and conclusionsConditionalsConnectivesSyllogismsDefinitionsCounterexamples

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