The proposition $(\sim p) \vee (p \wedge \sim q)$ is equivalent to

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

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

The negative of the statement $\sim p \wedge (p \vee q)$ is

Given below are two statements:
$p: 25 \text{ is a multiple of } 5.$
$q: 25 \text{ is a multiple of } 8.$
Write the compound statements connecting these two statements with "And" and "Or". In both cases,check the validity of the compound statement.

The negation of the statement "If India wins the match,then India will reach the final" is: