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The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :
$(\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \wedge \mathrm{p})$
$(\mathrm{q} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$
$(\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})$
$(\mathrm{p} \wedge \mathrm{r}) \Rightarrow(\mathrm{p} \wedge \mathrm{q})$
Solution
$(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$
$\sim(p \wedge q) \vee((r \wedge q) \wedge p)$
$\sim(p \wedge q) \vee((r \wedge p) \wedge(p \wedge q)$
$\Rightarrow[\sim(p \wedge q) \vee(p \wedge q)] \wedge(\sim(p \wedge q) \vee(r \wedge p))$
$\Rightarrow t \wedge[\sim(p \wedge q) \vee(r \wedge p)]$
$\Rightarrow \sim(p \wedge q) \vee(r \wedge p)$
$\Rightarrow(p \wedge q) \Rightarrow(r \wedge p)$
Aliter:
given statement says
" if $\mathrm{p}$ and $\mathrm{q}$ both happen then
$\mathrm{p}$ and $\mathrm{q}$ and $\mathrm{r}$ will happen"
it Simply implies
"If $\mathrm{p}$ and $\mathrm{q}$ both happen then
'r' too will happen "
i.e.
" if $\mathrm{p}$ and $\mathrm{q}$ both happen then $\mathrm{r}$ and $\mathrm{p}$ too will happen
i.e.
$(p \wedge q) \Rightarrow(r \wedge p)$
