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 $B\,\subset\,D,$ 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 $A\,⊈\,B$ and $B\,⊈\,D$

Answer 1

Answer: (D)

Contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$
$\left(A\subseteq B\right)\Lambda\left(B\subseteq D\right) \rightarrow\left(A\subseteq C\right)$
Contrapositive is
$\sim\left(A\subseteq C\right) \rightarrow \left(A\subseteq B\right)\vee\sim\left(B\subseteq D\right)$
$A⊈C \rightarrow (A⊈ B)\vee(B ⊈ D) $