Deductive Reasoning Flashcards

All mammals are warm-blooded. No reptiles are warm-blooded. Which conclusion must follow?

Answer: No reptiles are mammals

Since all mammals are warm-blooded and no reptiles are warm-blooded, no reptile can be a mammal.

If it is raining, the ground is wet. The ground is not wet. What must be true?

Answer: It is not raining

This is modus tollens: denying the consequent (ground not wet) allows us to deny the antecedent (not raining).

Every student who passed the exam studied for at least five hours. Mia did not study for five hours. What can be concluded?

Answer: Mia did not pass the exam

Because studying five or more hours is necessary to pass, failing to meet that condition means Mia could not have passed.

All A are B. All B are C. Which statement is necessarily true?

Answer: All A are C

The chain All A→B and All B→C yields All A→C by the hypothetical syllogism.

Either the server is down or the network is broken. The network is not broken. What follows?

Answer: The server is down

Disjunctive syllogism: when one disjunct is false, the other must be true.

No licensed drivers are under 16 years old. Jordan is 14 years old. What must be true?

Answer: Jordan is not a licensed driver

Because Jordan is under 16 and no one under 16 is a licensed driver, Jordan is not licensed.

If a number is divisible by 6, it is divisible by both 2 and 3. The number 18 is divisible by 6. What follows?

Answer: 18 is divisible by both 2 and 3

Modus ponens applies: the antecedent is confirmed, so the consequent (divisibility by 2 and 3) must hold.