Suppose You Wish to Prove a Theorem of the Form

question 151

Short Answer

Suppose you wish to prove a theorem of the form "if p then q." (a) If you give a direct proof, what do you assume and what do you prove? (b) If you give a proof by contraposition, what do you assume and what do you prove? (c) If you give a proof by contradiction, what do you assume and what do you prove?

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Definitions:

Beliefs

Cognitive content held as true by an individual or group, often without empirical evidence.

Attitudes

An individual's evaluations, feelings, and tendencies toward an object or idea, which can influence behavior and perceptions.

Rationalize Occurrences

The process of providing reasonable explanations for events, often to justify one's own behavior or beliefs, even if the explanations are not based on facts.

Nonsense Syllable

A string of letters or sounds that does not have a meaning in any language, often used in memory and learning experiments.