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📐 Mathematics  ·  Sets  ·  JEE

By De Morgan’s law, (A ∪ B)′ equals:

Answer: A′ ∩ B′.

  • A A′ ∩ B′
  • B A′ ∪ B′
  • C A ∩ B
  • D A ∪ B

Correct answer: A. A′ ∩ B′

Explanation: The complement of a union is the intersection of the complements.

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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