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
If $\mathrm{A} \subseteq \mathrm{C},$ then $\mathrm{B} \subset \mathrm{A}$ or $\mathrm{D} \subset \mathrm{B}$
If $\mathrm{A} \ne \mathrm{C},$ then $\mathrm{A} \neq \mathrm{B}$ or $\mathrm{B} \ne \mathrm{D}$
If $\mathrm{A}\ne\mathrm{C},$ then $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D}$
If $\mathrm{A} \neq \mathrm{C},$ then $\mathrm{A} \neq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D}$
The negative of the statement $\sim p \wedge(p \vee q)$ is
Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.
Among the statements:
$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$
$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$
If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?
Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to