The statement pattern (p wedge q) wedge [(p w | vedclass

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(B) Given expression: $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ Using the distributive law on the term inside the square brackets: $

Vedclass · Accepted Answer

$p \wedge q$

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(B) Given expression: $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ Using the distributive law on the term inside the square brackets: $(p \wedge q) \vee (\sim p \wedge q) \equiv (p \vee \sim p) \wedge q$ Since $(p \vee \sim p) \equiv T$ (Tautology),we have: $T \wedge q \equiv q$ Substituting this back into the original expression: $(p \wedge q) \wedge q$ Using the associative and idempotent laws: $p \wedge (q \wedge q) \equiv p \wedge q$ Thus,the expression is equivalent to $p \wedge q$.

The statement pattern $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ is equivalent to

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