Mathematical Reasoning
Logical Equivalence / Negation
nta_pyq_2023_jan
Grade 11
Question:
Let $p$ and $q$ be two statements. Then $\sim(p \wedge (p \Rightarrow \sim q))$ is equivalent to
p ∨ (p ∧ (¬q))
p ∨ ((¬p) ∧ q)
(¬p) ∨ q
p ∨ (p ∧ q)
Step-by-Step Solution
Key Concept: Use De Morgan's law: $\sim(p\wedge(p\Rightarrow\sim q))=\sim p \vee \sim(\sim p \vee \sim q)=\sim p \vee (p\wedge q)$.
$\sim(p\wedge(\sim p\vee\sim q))=\sim p \vee(p\wedge q)=(\sim p\vee p)\wedge(\sim p\vee q)=\sim p\vee q$.
Correct Answer: 3