Prove That $A \cap ( B \cup C ) = ( A \cap B ) \cup ( A \cap C )$

question 192

Short Answer

Prove that $A \cap ( B \cup C ) = ( A \cap B ) \cup ( A \cap C )$ by giving a containment proof (that is, prove that the left side is a subset of the right side and that the right side is a subset of the left side).

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Definitions:

Variable Ratio Schedules

A reinforcement schedule in operant conditioning where a response is reinforced after an unpredictable number of responses, leading to high and steady response rates.

Reinforcement Theory

A behavioral theory proposing that behavior is a function of its consequences, with behaviors being encouraged or discouraged through positive or negative reinforcement.

Behavior

The actions or reactions of a person or animal in response to external or internal stimuli.

Need-Based Theories

Are theories of motivation that focus on what motivates a person, rather than on how that motivation occurs.