Mathematical Reasoning
Negation of Compound Statement
nta_pyq_2023_jan
Grade 11
Question:
The negation of the expression $q \vee ((\sim q) \wedge p)$ is equivalent to
$(\sim p) \wedge (\sim q)$
$p \wedge (\sim q)$
$(\sim p) \vee (\sim q)$
$(\sim p) \vee q$
Step-by-Step Solution
Key Concept: Apply De Morgan: $\sim(q\vee(\sim q\wedge p))=\sim q\wedge\sim(\sim q\wedge p)=\sim q\wedge(q\vee\sim p)=(\sim q\wedge\sim p)$.
$\sim(q\vee(\sim q\wedge p))=\sim q\wedge\sim(\sim q\wedge p)=\sim q\wedge(q\vee\sim p)=(\sim q\wedge q)\vee(\sim q\wedge\sim p)=(\sim q\wedge\sim p)$.
Correct Answer: 1