JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Mathematical Reasoning *

An implication $p\to (\sim q\vee r)$ is false only when its hypothesis is true and its conclusion is false. So $p$ must be $T$, and $\sim q\vee r$ must be $F$, which requires both $\sim q$ to be $F$ (hence $q$ is $T$) and $r$ to be $F$. The truth values of $p,q,r$ are therefore $T,T,F$.