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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

If A = \ 1, 3, 5, 7, 9, 11, 13, 15\ , B = \ 2, 4, , 16\ and N is...

If A={1,3,5,7,9,11,13,15},B={2,4,…,16}A = \left\{1, 3, 5, 7, 9, 11, 13, 15\right\}, B = \left\{2, 4, \ldots , 16\right\} and NN is the universal set, then A′∪((A∪B)∩B′){A}^{′} \cup \left(\left(A \cup B\right) \cap {B}^{′}\right) is (where, NN is the set of natural numbers)

Options

  1. AAA
  2. BNN
  3. CBB
  4. DNone of these

Correct answer

B. NN

Step-by-step solution

We know that,
(A∪B)∩B′=A\left(A \cup B\right) \cap {B}^{′} = A (as, A∩B=ϕA \cap B = ϕ)
So, \left[\left(A \cup B\right) \cap {B}^{′}\right] \cup {A}^{′} = A \cup {A}^{′} = N
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