JEE PYQ: Mathematical Reasoning Question 22
Question 22 - 2020 (07 Jan Shift 2)
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) If $A \not\subseteq C$, then $A \subseteq B$ and $B \subseteq D$
(2) If $A \subseteq C$, then $B \subset A$ or $D \subset B$
(3) If $A \not\subseteq C$, then $A \not\subseteq B$ and $B \subseteq D$
(4) If $A \not\subseteq C$, then $A \not\subseteq B$ or $B \not\subseteq D$
Type: MCQ
Show Answer
Answer: (4)
Solution
Let $P = A \subseteq B$, $Q = B \subseteq D$, $R = A \subseteq C$. Contrapositive of $(P \wedge Q) \to R$ is $\sim R \to \sim(P \wedge Q) = \sim R \to \sim P \vee \sim Q$.
BETA
