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📐 Mathematics  ·  Sets  ·  JEE

The number of subsets of a 5-element set that contain at least 3 elements is:

Answer: 16.

  • A 10
  • B 16
  • C 20
  • D 26

Correct answer: B. 16

Explanation: C(5,3) + C(5,4) + C(5,5) = 10 + 5 + 1 = 16.

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 →