Which of the following statements is $NOT$ logically equivalent to $\left( {p \to \sim p} \right) \to \left( {p \to q} \right)$?
$\left( {p \to p} \right) \to \left( {p \to \sim p} \right)$
$q \to \left( {p \to q} \right)$
$\left( {q \to \sim p} \right) \to \left( {q \to p} \right)$
none of these
If $p$ and $q$ are simple propositions, then $p \Rightarrow q$ is false when
$\left( {p \wedge \sim q \wedge \sim r} \right) \vee \left( { \sim p \wedge q \wedge \sim r} \right) \vee \left( { \sim p \wedge \sim q \wedge r} \right)$ is equivalent to-
Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is
Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard
The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to