JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 90

$(\sim p\to q)\to q$ fails only when $\sim p\to q$ is true and $q$ is false, i.e. $q$ false and $p$ true. In that case $p\to q$ is false, so the whole implication is true. In every other case it is true too: the statement is a tautology.