Which of the following Boolean expressions is not a tautology?
Correct Option: , 4
(1) $(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$
$=(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{q} \vee \mathrm{p})$
$=(\sim \mathrm{p} \vee \mathrm{p}) \vee \mathrm{q}$
$=\mathrm{t} \vee \mathrm{q}=\mathrm{t}$
$(2)(\mathrm{q} \rightarrow \mathrm{p}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$
$=(\sim \mathrm{q} \vee \mathrm{p}) \vee(\mathrm{q} \vee \mathrm{p})$
$=(\sim \mathrm{q} \vee \mathrm{q}) \vee \mathrm{p}$
$=\mathrm{t} \vee \mathrm{p}=\mathrm{t}$
(3) $(\mathrm{p} \rightarrow \sim \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$
$=(\sim \mathrm{p} \vee \sim \mathrm{q}) \vee(\mathrm{q} \vee \mathrm{p})$
$=(\sim \mathrm{p} \vee \mathrm{p}) \vee(\sim \mathrm{q} \vee \mathrm{q})$
$=\mathrm{t} \vee \mathrm{t}=\mathrm{t}$
(4) $(\sim \mathrm{q} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$
$=(p \vee q) \vee(q \vee p)$
$=(p \vee p) \vee(q \vee p)$
$=\mathrm{p} \vee \mathrm{q}$
Which is not a tautology.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.