If the statements $p, q$ and $r$ have the truth values $F, T, F$ respectively, then the truth values of the…

If the statements $p, q$ and $r$ have the truth values $F, T, F$ respectively, then the truth values of the statement patterns $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are respectively
  1. $\mathrm{T}, \mathrm{T}$
  2. $\mathrm{T}, \mathrm{F}$
  3. $\mathrm{F}, \mathrm{T}$
  4. F, F

Solution

$\begin{aligned} & (p \wedge \sim q) \rightarrow r \\ & \equiv(F \wedge \sim T) \rightarrow F \\ & \equiv(F \wedge F) \rightarrow F \\ & \equiv F \rightarrow F \\ & \equiv T \end{aligned}$
Consider $(p \vee q) \rightarrow r$ $\begin{aligned} & \equiv(\mathrm{F} \vee \mathrm{~T}) \rightarrow \mathrm{F} \\ & \equiv \mathrm{~T} \rightarrow \mathrm{~F} \\ & \equiv \mathrm{~F} \end{aligned}$ Truth values of $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are T and F respectively.

Asked in: MHT CET 2024 (04 May Shift 2)

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