The statement $[(p \wedge  q) \rightarrow p] \rightarrow (q \wedge  \sim q)$ is

Which of the following is always true

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

Which of the following  statements is $NOT$  logically equivalent to $\left( {p \to  \sim p} \right) \to \left( {p \to q} \right)$?

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.