$( S 1)( p \Rightarrow q ) \vee( p \wedge(\sim q ))$ is a tautology $( S 2)((\sim p ) \Rightarrow(\sim q )) \wedge((\sim p ) \vee q )$ is a Contradiction. Then

$\sim (p \vee q)$ is equal to

$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to

The negation of the statement

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

For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p\, \wedge \,q)$ is 

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