JEE Main 2019 — Mathematical Reasoning Question with Solution

$q$ is false and $[(p\wedge q)\leftrightarrow r]$ is true As $(p\wedge q)$ is false $[$ False $\leftrightarrow r]$ is true Hence $r$ is false Option (1): says $p\vee r$, Since $r$ is false Hence $(p\vee r)$ can either be true or false Option (2): says $(p\wedge r)\to (p\vee r)$ $(p\wedge r)$ is false Since, $F\to T$ is true and $F\to F$ is also true Hence, it is a tautology Option (3): $(p\vee r)\to (p\wedge r)$ i.e. $(p\vee r)\to F$ It can either be true or false Option (4): $(p\wedge r)$ Since, $r$ is false Hence, $(p\wedge r)$ is false.