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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

Let n ( A ) denotes the number of elements in the set A . If n(A) =...

Let n(A)n ( A ) denotes the number of elements in the set AA. If n(A)=4,n(B)=5n\left(A\right) = 4, n\left(B\right) = 5 and n(A∩B)=3n\left(A \cap B\right) = 3, then n[(A×B)∩(B×A)]n [ ( A \times B ) \cap ( B \times A ) ] is equal to

Options

  1. A88
  2. B99
  3. C1010
  4. D1111

Correct answer

B. 99

Step-by-step solution

Given, n(A)=4,n(B)=5n\left(A\right) = 4, n\left(B\right) = 5 and n(A∩B)=3n\left(A \cap B\right) = 3

∴n[(A×B)∩(B×A)]=n[(A∩B)×(B∩A)]=32=9∴ n\left[\left(A \times B\right) \cap \left(B \times A\right)\right] = n\left[\left(A \cap B\right) \times \left(B \cap A\right)\right] = {3}^{2} = 9
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