# If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is ______. - Mathematics

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If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is ______.

• Φ

• N

• A

• B

#### Solution

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is N.

Explanation:

Given that, A = {1, 3, 5, 7, 9, 11, 13, 15, 17}

B = {2, 4, ..., 18}

U = N = {1, 2, 3, 4, 5, ...}

A' ∪ (A ∪ B) ∩ B' = A' ∪ [(A ∩ B') ∪ (B ∩ B')]

= A' ∪ (A ∪ B') ∩ Φ   ......[∵ A ∩ A' = Φ]

= A' ∪ (A ∩ B')

= (A' ∪ A) ∩ (A' ∪ B')

= N ∩ (A' ∪ B')   ......[∵ A' ∪ A = N]

= A' ∪ B'

= (A ∩ B)'

= (Φ)'

= N   ......[∵ A ∩ B = Φ]

Concept: Types of Sets - Universal Set
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 1 Sets
Exercise | Q 41 | Page 17

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