When does the current flow through the following circuit

$\sim (p \vee (\sim q))$ is equal to .......

If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?

The logically equivalent of $p \Leftrightarrow q$ is :-

Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to

The negation of the statement $(( A \wedge( B \vee C )) \Rightarrow( A \vee B )) \Rightarrow A$ is