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The logical expression
$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{r})]$ is equivalent to
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$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \mathrm{r})]$ is equivalent to
Solution:
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Verified Answer
The correct answer is:
$\mathrm{q} \vee \mathrm{r}$
$[p \wedge(q \vee r)] \vee[(\sim p \wedge q) \vee(\sim p \wedge r)]$
$\equiv[p \wedge(q \vee r)] \vee[\sim p \wedge(q \vee r)]$
$\equiv(q \vee r) \wedge(p \vee \sim p)$
$\equiv(q \vee r) \wedge T$
$\equiv q \vee r$
$\equiv[p \wedge(q \vee r)] \vee[\sim p \wedge(q \vee r)]$
$\equiv(q \vee r) \wedge(p \vee \sim p)$
$\equiv(q \vee r) \wedge T$
$\equiv q \vee r$
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