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📐 Mathematics  ·  Sets  ·  JEE

The number of elements in the power set of the power set of the empty set is:

Answer: 2.

  • A 1
  • B 2
  • C 4
  • D 0

Correct answer: B. 2

Explanation: P(∅) = {∅} has 1 element, so P(P(∅)) has 2¹ = 2 elements.

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 →