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📐 Mathematics  ·  Sets  ·  JEE

The number of relations from a 3-element set to itself is:

Answer: 512.

  • A 64
  • B 256
  • C 512
  • D 9

Correct answer: C. 512

Explanation: A relation is any subset of the 3×3 = 9 ordered pairs, giving 2⁹ = 512.

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 →