Let A, B, C and D be four nonempty sets. The contrapositive of 'if $A \subseteq B$ and $B \subseteq D$ then…

Let A, B, C and D be four nonempty sets. The contrapositive of 'if $A \subseteq B$ and $B \subseteq D$ then $A \subseteq C$ ' is
  1. If $A \subseteq C$, then $A \subseteq B$ or $B \nsubseteq D$
  2. If $A \subset C$, then $A \subseteq B$ and $B \subseteq D$
  3. If $A \subseteq C$, then $A \subseteq B$ and $B \subseteq D$
  4. If $\mathrm{A} \subseteq C$, then $\mathrm{B} \subset \mathrm{A}$ or $\mathrm{D} \subset \mathrm{B}$

Solution

The contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$ so, the required contrapositive is If $A \nsubseteq C$, then $A \nsubseteq B$ or $B \nsubseteq D$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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