Q91 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

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

  • Correct answer
    A
    If $A \subseteq C$, then $A \subseteq B$ or $B \nsubseteq D$
  • B
    If $A \subset C$, then $A \subseteq B$ and $B \subseteq D$
  • C
    If $A \subseteq C$, then $A \subseteq B$ and $B \subseteq D$
  • D
    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 $B \nsubseteq D$

Hence, the correct answer is option: 'A'.

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