Q165 / 270 · NDA 2022 (Phase 2) · Mathematics

Consider the following : 1. $A \cap B=A \cap C \Rightarrow B=C$ 2. $A \cup B=A \cup C \Rightarrow B=C$ Which of the above is/are correct?

  • A
    1 only
  • B
    2 only
  • C
    Both 1 and 2
  • Correct answer
    D
    Neither 1 nor 2

Solution

Let $A=\{1,2\}, B=\{2,3\}, C=\{2,4\}$ $\therefore \quad A \cap B=A \cap C=\{2\}$ But $B \neq C$ So, statement 1 is wrong Let $A=\{1,2\}, B=\{2,3\}, C=\{1,2,3\}$ $\therefore \quad A \cup B=A \cup C=\{1,2,3\}$ But $B \neq C$. So, statement 2 is wrong.

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

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