The negation of the statement

"If I become a teacher, then I will open a school", is

The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to

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

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then