Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively

Which of the following is a contradiction

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

Among the two statements

$(S1):$ $( p \Rightarrow q ) \wedge( q \wedge(\sim q ))$ is a contradiction and

$( S 2):( p \wedge q ) \vee((\sim p ) \wedge q ) \vee$

$( p \wedge(\sim q )) \vee((\sim p ) \wedge(\sim q ))$ is a tautology

Let $*, \square \in\{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p} * \sim \mathrm{q}) \Rightarrow(\mathrm{p} \square \mathrm{q})$ is a tautology. Then :

If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is