Question

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

• A. $q$
• B. $p \wedge q$
• C. $p$
• D. $p \vee q$

Hint:

Use the absorption law shortcut: Let $A = p \wedge q$. The expression can be rewritten as $A \wedge [A \vee (\sim p \wedge q)]$. According to the absorption law, $A \wedge (A \vee B) \equiv A$ for any compound statement $B$. This gives the answer $A = p \wedge q$ instantly!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Simplify the logical expression [(p∧q)∨(~p∧q)] ∧ (p∧q).

Step 2: Key Formula or Approach:
Use distributive and absorption laws of Boolean algebra.

Step 3: Detailed Explanation:
Bracket = (p∨~p)∧q ≡ T∧q ≡ q. Full expression = q ∧ (p∧q) ≡ p∧(q∧q) ≡ p∧q.

Step 4: Final Answer:
The simplified expression is p∧q, matching option (B).