The contrapositive of the statement "I go to school if it does not rain" is

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 Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:

Which of the following statements is a tautology?

The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ is

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