Zaymiey

📐 Mathematics  ·  Sets  ·  JEE

If n(A ∪ B) = 12, n(A) = 8 and n(B) = 6, then n(A ∩ B) equals:

Answer: 2.

  • A 0
  • B 2
  • C 4
  • D 6

Correct answer: B. 2

Explanation: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 8 + 6 − 12 = 2.

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 →