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📐 Mathematics  ·  Sets  ·  JEE

For any set A, which is always true?

Answer: Empty set is a subset of A.

  • A A subset of empty set
  • B Empty set is a subset of A
  • C A = empty set
  • D A subset of A'

Correct answer: B. Empty set is a subset of A

Explanation: The empty set is a subset of every set, including A. This is a universal rule.

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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