The negation of the statement $q \wedge \left( { \sim p \vee \sim r} \right)$
$ \sim q \vee \left( {p \wedge r} \right)$
$ \sim q \vee \left( {p \wedge \sim r} \right)$
$ \sim q \wedge \left( { \sim p \wedge r} \right)$
$ \sim q \wedge \left( {p \wedge \sim r} \right)$
$(p \to q) \leftrightarrow (q\ \vee \sim p)$ is
Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ be four non-empty sets. The contrapositive statement of "If $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D},$ then $\mathrm{A} \subseteq \mathrm{C}^{\prime \prime}$ is
The propositions $(p \Rightarrow \;\sim p) \wedge (\sim p \Rightarrow p)$ is a
Negation of $p \wedge( q \wedge \sim( p \wedge q ))$ is
$(p \wedge \, \sim q)\, \wedge \,( \sim p \vee q)$ is :-