Q60 / 170 · Manipal (MET) 2018 · Mathematics

The negation of the compound proposition $p \vee(\sim p \vee q)$ is

  • Correct answer
    A
    $(p \wedge \sim q) \wedge \sim p$
  • B
    $(p \wedge \sim q) \vee \sim p$
  • C
    $(p \wedge \sim q) \vee \sim p$
  • D
    None of the above

Solution

The negation of the compound proposition \(p \wedge(\sim p \vee q)\) is, \(\begin{aligned} & \equiv \sim(p \wedge(\sim p \vee q)) \equiv \sim p \vee \sim(\sim p \vee q) \\ & \equiv \sim p \vee(p \wedge \sim q) \equiv(p \wedge \sim q) \vee \sim p \end{aligned}\)

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

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