If q is false and p q rightarrow r is true, then which one of the...

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 $(p \wedge r) \rightarrow(p \vee r) (p \wedge r)$ is false Since, $F \rightarrow T$ is true and $F \rightarrow F$ is also true Hence, it is a tautology Option (3): $(p \vee r) \rightarrow(p \wedge r)$ i.e. $(p \vee r) \rightarrow F$ It can either be true or false Option (4): $(p \wedge r)$ Since, $r$ is false Hence, $(p \wedge r)$ is false.