Zaymiey

📐 Mathematics  ·  Sets  ·  JEE

In the inclusion–exclusion formula, n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(C∩A) + :

Answer: n(A∩B∩C).

  • A n(A∩B∩C)
  • B 0
  • C n(A∪B∪C)
  • D 1

Correct answer: A. n(A∩B∩C)

Explanation: The triple-overlap term n(A ∩ B ∩ C) is added back at the end.

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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