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:

Social Learning Theory

A theory that suggests people learn new behaviors through observational learning of others' actions and consequences.

Observation and Imitation

A method of learning in which an individual observes the actions of others and mimics them, crucial in the acquisition of new behaviors.

Gender-Appropriate Behavior

Actions and manners deemed suitable for an individual based on societal norms related to their gender.

Behavior Modification

Techniques and therapies used to change undesirable behaviors into desirable ones through reinforcement and punishment.