The Boolean expression (mathrm{p} wedge mathr | vedclass

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Question

$(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$

$\sim(p \wedge q) \vee((r \wedge q) \wedge p)$

$\sim(p \wedge q) \vee((r \wedge p) \wedge(p \wedge

Vedclass · Accepted Answer

$(\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \wedge \mathrm{p})$

Vedclass · Answer

$(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$

$\sim(p \wedge q) \vee((r \wedge q) \wedge p)$

$\sim(p \wedge q) \vee((r \wedge p) \wedge(p \wedge q)$

$\Rightarrow[\sim(p \wedge q) \vee(p \wedge q)] \wedge(\sim(p \wedge q) \vee(r \wedge p))$

$\Rightarrow t \wedge[\sim(p \wedge q) \vee(r \wedge p)]$

$\Rightarrow \sim(p \wedge q) \vee(r \wedge p)$

$\Rightarrow(p \wedge q) \Rightarrow(r \wedge p)$

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.

$(p \wedge q) \Rightarrow(r \wedge p)$

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :