Deductive Reasoning Flashcards

The argument form 'P → Q; P; therefore Q' is called:

Answer: Modus ponens

Modus ponens (affirming the antecedent) concludes Q when both P→Q and P are given.

Some athletes are vegetarians. All vegetarians avoid red meat. Which conclusion must be true?

Answer: Some athletes avoid red meat

The vegetarian athletes (some athletes) must avoid red meat, making 'some athletes avoid red meat' necessarily true.

If a syllogism has a true conclusion, it must be valid. Which statement best identifies the flaw in this claim?

Answer: A true conclusion can result from an invalid argument

An invalid argument can accidentally produce a true conclusion; validity concerns the argument's structure, not the conclusion's truth value.

No one who cheats on exams graduates with honors. Taylor graduated with honors. What follows?

Answer: Taylor did not cheat on exams

Modus tollens: honors graduation is incompatible with cheating, so an honors graduate cannot be a cheater.

All X are Y. No Y are Z. Which conclusion follows with certainty?

Answer: No X are Z

X is a subset of Y, and Y excludes Z entirely; therefore X, being within Y, must also exclude Z.

A deductive argument is 'sound' if and only if it is:

Answer: Valid with all true premises

Soundness requires both validity (correct logical structure) and all premises being actually true.

If P then Q. If Q then R. P is true. What must be true?

Answer: Both Q and R are true

P→Q with P true gives Q; Q→R with Q true gives R; both conclusions hold by successive modus ponens.