Which of the following is always true

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is

If $p, q, r$ are simple propositions with truth values $T, F, T$, then the truth value of $(\sim p \vee q)\; \wedge \sim r \Rightarrow p$ is

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow(( p \nabla$q) $\nabla r$ ) is a tautology. Then (p $\nabla q ) \Delta r$ is logically equivalent to

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