Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ be three statements, then $[\mathrm{p} \rightarrow(\mathrm{q}…
Let $\mathrm{p}, \mathrm{q}, \mathrm{r}$ be three statements, then $[\mathrm{p} \rightarrow(\mathrm{q} \rightarrow \mathrm{r})] \leftrightarrow[(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r}]$ is
equivalent to $\mathrm{p} \leftrightarrow \mathrm{q}$.
contingency.
tautology.
contradiction.
Solution
Given statement,
$\begin{aligned}
{[p \rightarrow(q \rightarrow r)] } & \leftrightarrow[(p \wedge q) \rightarrow r] \\
p \rightarrow(q \rightarrow r) & \equiv \sim p \vee(q \rightarrow r) \\
& \equiv \sim p \vee(\sim q \vee r) \\
& \equiv[(\sim p) \vee(-q)] \vee r ... [\text { Associative law}]\\
& \equiv \sim(p \wedge q) \vee r \quad \ldots[\text { De'morgans law }] \\
& \equiv p \wedge q \rightarrow r
\end{aligned}$
$\therefore$Given statement is tautology.