The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow[(\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q}]$ is :

(C) equivalent to $\sim p \rightarrow q$

(D) equivalent to $\mathrm{p} \rightarrow \sim \mathrm{q}$

JEE Main · 2017 · 02 Apr 2017 · Offline · Mathematical Reasoning *

The following statement

(p \to q) \to [(\sim p \to q) \to q]

is :

Answer: (B)

Build the truth table for

(p \to q) \to [(\sim p \to q) \to q]

. Running through all four combinations of

p

and

q

, the whole expression comes out true in every row. A statement true under every assignment is a tautology.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option