If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $p, q, r$ are…

If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $p, q, r$ are respectively.
  1. F, F, T
  2. F, T, F
  3. T, F, F
  4. $\quad \mathrm{T}, \mathrm{T}, \mathrm{F}$

Solution

Given that \(\begin{array}{ll} & (p \wedge \sim r) \rightarrow(\sim p \vee q) \equiv F \\ \therefore & \sim p \vee q \equiv F \\ \therefore & \sim p \equiv F \text { and } q \equiv F \\ \therefore & p=T \text { and } q=F \\ \therefore & \text { Option }(C) \text { is correct. } \end{array}\)

Asked in: MHT CET 2024 (10 May Shift 2)

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