Mathematical Reasoning
Logical Equivalence / Truth Tables
nta_pyq_2023_jan
Grade 11
Question:
The compound statement $(\sim(P \wedge Q)) \vee ((\sim P) \wedge Q) \Rightarrow ((\sim P) \wedge (\sim Q))$ is equivalent to
$((\sim P) \vee Q) \wedge ((\sim Q) \vee P)$
$(\sim Q) \vee P$
$((\sim P) \vee Q) \wedge (\sim Q)$
$(\sim P) \vee Q$
Step-by-Step Solution
Key Concept: Construct truth table for the compound statement and match with options.
Truth table shows the compound implication is equivalent to $((\sim P)\vee Q)\wedge((\sim Q)\vee P)$.
Correct Answer: 1