The statement pattern $[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]$ is equivalent to
The statement pattern $[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]$ is equivalent to
- $q \vee r$
- $\mathrm{p} \vee \mathrm{r}$.
- q
- p
Solution
$\begin{aligned}
& {[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]} \\
& \equiv[p \wedge(q \vee r)] \vee[p \wedge(\sim r \wedge \sim q)]\ldots \text{ [Commutativity and associativity]}
\end{aligned}$
$\equiv[p \wedge(q \vee r)] \vee[p \wedge \sim(r \vee q)... \text{ [DeMorgan's Law]}$
$\begin{aligned}
& \equiv p \wedge[(q \vee r) \vee \sim(q \vee r)] \ldots \text{...[Distributive and commutative Law]}\\
& \equiv p \wedge T \lsts \text{...[Absorption Law]}
\end{aligned}
$\equiv \mathrm{p}$ ...[Identity Law]
Asked in: MHT CET 2024 (04 May Shift 1)
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