The statement [p wedge (q vee r)] vee [sim r | vedclass

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(B) Given expression: $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$Using the commutative law on the second part: $[p \wedge (q \vee r)]

Vedclass · Accepted Answer

$p$

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(B) Given expression: $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$Using the commutative law on the second part: $[p \wedge (q \vee r)] \vee [p \wedge \sim q \wedge \sim r]$Applying De Morgan's law to the second part: $[p \wedge (q \vee r)] \vee [p \wedge \sim (q \vee r)]$Using the distributive law: $p \wedge [(q \vee r) \vee \sim (q \vee r)]$Using the complement law: $p \wedge T$ (where $T$ is a tautology)Using the identity law: $p$Therefore,the statement is equivalent to $p$.

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

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