If the Boolean expression $( p \wedge q ) \circledast( p \otimes q )$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

Which of the following is always true

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

Which of the following is not a statement

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is