Among the statements : [(S 1)~((p q) r) (p r)] [(S 2)~((p q) r) ((p r) (q r))]

Question

Among the statements :

$$(\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})$$

$$(\mathrm{S} 2)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow((\mathrm{p} \Rightarrow \mathrm{r}) \vee(\mathrm{q} \Rightarrow \mathrm{r}))$$

Accepted Answer

$${S1}:\left( {(p \vee q) \Rightarrow r} \right) \Leftrightarrow (p \Rightarrow r)$$

$${S2}:\left( {(p \vee q) \Rightarrow r} \right) \Leftrightarrow \left( {(p \Rightarrow r) \vee (q \Rightarrow r)} \right)$$

In $S1:$ If $p=F, q=T, r=F$ then $S_1$ is false

In $S2:$ If $p=T, q=F, r=F$ then $S_2$ is false

$$\therefore$$ Neither S1 nor S2 is a tautology

Solutions · 1