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📐 Mathematics  ·  Sets  ·  JEE

The identity n(A∪B) = n(A) + n(B) − n(A∩B) is known as the:

Answer: the inclusion–exclusion principle.

  • A the associative law of sets
  • B the inclusion–exclusion principle
  • C the distributive law of sets
  • D De Morgan’s second law

Correct answer: B. the inclusion–exclusion principle

Explanation: This is the inclusion–exclusion principle: adding the two sizes double-counts the overlap, so it is subtracted once.

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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