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📐 Mathematics  ·  Sets  ·  JEE

In a survey of 100 people, 60 read A, 50 read B and 30 read both. The number reading at least one is:

Answer: 80.

  • A 80
  • B 90
  • C 110
  • D 30

Correct answer: A. 80

Explanation: n(A ∪ B) = 60 + 50 − 30 = 80.

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

Read the full Sets notes →