Q97 / 150 · MHT CET 2024 (03 May Shift 2) · Mathematics

$\sim[(p \vee \sim q) \rightarrow(p \wedge \sim q)] \equiv$

  • A
    $(p \wedge \sim q) \wedge(\sim p \vee q)$
  • B
    $(p \wedge \sim q) \wedge(\sim p \wedge q)$
  • Correct answer
    C
    $(p \vee \sim q) \wedge(\sim p \vee q)$
  • D
    $(p \vee \sim q) \vee(\sim p \vee q)$

Solution

$\begin{aligned} & \sim[(p \vee \sim q) \rightarrow(p \wedge \sim q)] \\ & \equiv \sim[\sim(p \vee \sim q) \vee(p \wedge \sim q)] \ldots[\text { Conditional law }]\end{aligned}$ $\begin{array}{ll}\equiv(p \vee \sim q) \wedge \sim(p \wedge \sim q) & \ldots[\text { De Morgan's law }] \\ \equiv(p \vee \sim q) \wedge(\sim p \vee q) & \ldots[\text { De Motgan's law }]\end{array}$

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

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