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

Question

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 (A) φ (B) N (C) A (D) B

Tardigrade Admin · Accepted Answer

A' ∪ ( (A ∪ B) ∩ B') = A' ∪ (A ∪ (B ∩ B')) = A' ∪ (A ∪ φ ) = A' ∪ A = N (∵ B ∩ B' = φ)

Q. 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 $A^{'} \cup ((A \cup B) \cap B^{'})$ is

$ϕ$

$N$

$A$

$B$

$A^{'} \cup ((A \cup B) \cap B^{'}) = A^{'} \cup (A \cup (B \cap B^{'}))$
$= A^{'} \cup (A \cup ϕ) = A^{'} \cup A = N (∵ B \cap B^{'} = ϕ)$

Q. 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

A′∪((A∪B)∩B′)=A′∪(A∪(B∩B′)) =A′∪(A∪ϕ)=A′∪A=N(∵B∩B′=ϕ)

Q. 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 $A^{'} \cup ((A \cup B) \cap B^{'})$ is

$ϕ$

$N$

$A$

$B$

$A^{'} \cup ((A \cup B) \cap B^{'}) = A^{'} \cup (A \cup (B \cap B^{'}))$
$= A^{'} \cup (A \cup ϕ) = A^{'} \cup A = N (∵ B \cap B^{'} = ϕ)$