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📐 Mathematics  ·  Sets  ·  JEE

In a survey of 100 people, 60 like tea, 50 like coffee and 30 like both. The number liking neither is:

Answer: 20.

  • A 10
  • B 20
  • C 30
  • D 40

Correct answer: B. 20

Explanation: Liking at least one = 60 + 50 − 30 = 80, so neither = 100 − 80 = 20.

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 →