The number of values of r p, q, p, q for which ((p q) (r q)) ((p r) q) is a tautology, is …

Question

The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \mathrm{q})$ is a tautology, is :

Accepted Answer

$((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q) \equiv T$ (given)

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

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

$\equiv \sim p \vee \sim r \vee q$

For above statement to be tautology

$r$ can be $\sim p$ or $q$

$	herefore $ Two values of $r$ are possible.

Solutions · 1