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📐 Mathematics  ·  Sets  ·  JEE

If n(A) = 5, n(B) = 3 and n(A ∩ B) = 2, then n(A ∪ B) is:

Answer: 6.

  • A 6
  • B 8
  • C 10
  • D 4

Correct answer: A. 6

Explanation: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 5 + 3 − 2 = 6.

Set Operations: Union, Intersection, ComplementUABA∩BOutside both circles = (A∪B)' = A'∩B' (De Morgan)A∪B = everything in either circle; A∩B = only the overlap

A Venn diagram makes set identities visual: A∪B is everything inside either circle, A∩B is only the overlap, and the region outside both circles represents the complement of their union - directly illustrating De Morgan's law (A∪B)′ = A′∩B′.

Concept context

Types of sets, operations (union/intersection/complement), relations, and types of functions with domain and range

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