Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11
Question:
Which of the following is incorrect?
$\sim(p \wedge q) \iff p \vee q$
$(p \Leftrightarrow q) \iff p \iff q$
$\sim(p \Rightarrow q) \equiv \sim p \Rightarrow q$
$\sim(p \Rightarrow q) \equiv p \wedge \sim q$
Step-by-Step Solution
Key Concept: Logical equivalence requires statements to have identical truth values under all conditions
Option (C) & (D) are theorems. Hence, (C) & (D) are correct. For option (A), $\neg (p \neg q) \equiv p \neg (\neg q) \equiv p \vee q$. Hence, (A) is correct. For option (B), when $p$ is true and $q$ is false then $p \neg q$ is true and $p \equiv q$ is false. Hence, option (B) is incorrect.
Correct Answer: 1