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

The expression $[(p \wedge \sim q) \vee q] \vee(\sim p \wedge q)$ is equivalent to
  1. $\mathrm{p} \vee \mathrm{q}$
  2. $\mathrm{p} \wedge \mathrm{q}$
  3. $\mathrm{p} \rightarrow \mathrm{q}$
  4. $\mathrm{p} \leftrightarrow \mathrm{q}$

Solution

$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \mathrm{p} & \mathrm{Q} & \sim \mathrm{p} & \sim \mathrm{q} & \mathrm{p} \vee \mathrm{q} & \mathrm{p} \wedge \mathrm{q} & \mathrm{p} \rightarrow \mathrm{q} & \mathrm{p} \leftrightarrow \mathrm{q} & 1 \wedge 4 & 2 \vee 9 & 2 \wedge 3 & 10 \vee 11 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \hline \end{array} $ Entries in columns 5 and 12 are identical.

Asked in: MHT CET 2021 (22 Sep Shift 1)

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