Q41 / 100 · BITSAT 2024 (Memory Based Paper 3) · Mathematics

The Boolean expression $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

  • A
    $p$
  • B
    $q$
  • C
    $\sim q$
  • Correct answer
    D
    $\sim p$

Solution

$\begin{aligned} & \text { Given, } \sim(p \vee q) \vee(\sim p \wedge q) \\ & \Rightarrow(\sim p \wedge \sim q) \vee(\sim p \wedge q) \text { (By De Morgan's Law) } \\ & \Rightarrow \sim p \wedge(\sim q \vee q) \text { (Distributive Law) } \\ & \Rightarrow \sim p \wedge t \text { (By complement law, where } t=\text { tautology) } \\ & \Rightarrow \sim p \text { (Identity law) }\end{aligned}$

Hence, the correct answer is option: 'D'.

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