Q32 / 100 · BITSAT 2023 (Memory Based Paper 2) · Mathematics
The negation of the Boolean expression $((\sim q)$ $\wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to
- A$p \Rightarrow q$
- B$q \Rightarrow p$
- Correct answerC$\sim(p \Rightarrow q)$
- D$\sim(q \Rightarrow p)$
Solution
Given boolen expression are
$\begin{aligned}<br />& \sim p \vee q \equiv p \rightarrow q \text { and } \sim q \wedge p \equiv \sim(p \rightarrow q) \\<br />& \text { Negation of } \sim(p \rightarrow q) \rightarrow(p \rightarrow q) \\<br />& \text { is } \sim(p \rightarrow q) \wedge(\sim(p \rightarrow q)) \text { i.e., } \sim(p \rightarrow q)<br />\end{aligned}$
$\begin{aligned}<br />& \sim p \vee q \equiv p \rightarrow q \text { and } \sim q \wedge p \equiv \sim(p \rightarrow q) \\<br />& \text { Negation of } \sim(p \rightarrow q) \rightarrow(p \rightarrow q) \\<br />& \text { is } \sim(p \rightarrow q) \wedge(\sim(p \rightarrow q)) \text { i.e., } \sim(p \rightarrow q)<br />\end{aligned}$
Hence, the correct answer is option: 'C'.