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NDA 2025 Maths · Mathematics · Sets, Relations and Functions · easy

For finite sets A,B, n(A∪ B)=n(A)+n(B) always. 2. The empty set is a subset of every set, and \∅\ has exactly one element.

Single correct option

Consider the following statements:
1. For finite sets A,BA,B, n(A∪B)=n(A)+n(B)n(A\cup B)=n(A)+n(B) always.
2. The empty set is a subset of every set, and {∅}\{\varnothing\} has exactly one element.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

Statement 1 is false unless A∩B=∅A\cap B=\varnothing; in general n(A∪B)=n(A)+n(B)−n(A∩B)n(A\cup B)=n(A)+n(B)-n(A\cap B). Statement 2 is true: ∅⊆S\varnothing\subseteq S for every set SS, and {∅}\{\varnothing\} is a set containing the single element ∅\varnothing.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake