The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is

If $A$ : Lotuses are Pink and $B$ : The Earth is a planet. Then the
verbal translation of $\left( { \sim A} \right) \vee B$ is

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to 

Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is

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