Let A, B, C and D be four non-empty sets.
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:

1. (1) If $A \not \subset C$, then $A \subseteq B$ and $B \subseteq D$

2. (2) If $A \subseteq C$, then $B \subset A$ or $D \subset B$

3. (3) If $A \not \subset$, then $A \not B$ and $B \subseteq D$

4. (4) If $A \not \subset$, then $A \not \subset B$ or $B \nsubseteq D$

Correct Option: , 4

Solution:

Let $P=A \subseteq B, Q=B \subseteq D, R=A \subseteq C$

Contrapositive of $(P \wedge Q) \rightarrow R$ is $\sim R \rightarrow \sim(P \wedge Q)$

$\sim R \rightarrow \sim P \vee \sim Q$