Question

Let $A,B,C$ and $D$be four non-empty sets. The contrapositive statement of “If $A\subseteq B$ and $B\subseteq D$ then $A\subseteq C$ ” is

• A. If$A\subseteq C$, then $B\subset A$ or $D\subset B$
• B. If $A⊈C$, then $A\subseteq B$ and $B\subseteq D$
• C. If $A⊈C$, then $A⊈B$ and $B\subseteq D$
• D. If $A⊈C,$ then $A⊈B$ or$B⊈D$

Answer 1

The correct option is D

If $A⊈C,$ then $A⊈B$ or$B⊈D$

Explanation for the correct option:

Finding the contrapositive statement of “If $A\subseteq B$ and $B\subseteq D$ then $A\subseteq C$ ”

Given: $A,B,C$ and $D$ are four non-empty sets.

Let $A\subseteq C=p$ ,$B\subseteq D=q$ and $A\subseteq C=r$

Contrapositive of $p\to q$ is $\sim q\to \sim p$
$(A\subseteq B)\mathrm{\Lambda }(B\subseteq D)\to (A\subseteq C)$
Contrapositive is$~(A\subseteq C)\to ~(A\subseteq B)\vee ~(B\subseteq D)$
$A⊈C\to (A⊈B)$ or $(B⊈D)$

Hence the correct option is (D)