- Home
- Standard 11
- Mathematics
निम्न में से कौनसा कथन पुनरूक्ति है?
$(\sim \mathrm{p}) \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$
$(\mathrm{q} \rightarrow \mathrm{p}) \vee \sim(\mathrm{p} \rightarrow \mathrm{q})$
$(p \rightarrow q) \wedge(q \rightarrow p)$
$(\sim \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
Solution
Option (1) is
$\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv(\sim \mathrm{p} \wedge \mathrm{p}) \vee(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv \mathrm{C} \vee(\sim \mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{q}$
$\equiv(\sim p \wedge q) \rightarrow q$
$\equiv \sim(\sim \mathrm{p} \wedge \mathrm{q}) \vee \mathrm{q}$
$\equiv(\mathrm{p} \vee \sim \mathrm{q}) \vee \mathrm{q}$
$\equiv(\mathrm{p} \vee \mathrm{q}) \vee(\sim \mathrm{q} \vee \mathrm{q})$
$\equiv(\mathrm{p} \vee \mathrm{q}) \vee \mathrm{t}$
so $\sim \mathrm{p} \wedge(\mathrm{p} \vee \mathrm{q}) \rightarrow \mathrm{q}$ is a tautology
