Q. 41

If A = {1, 3, 5, A. ϕ

B. N

C. A

D. B

Answer :

Given: A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ... , 18}


To find: A′ (A B) B′


A′ (A B) B′


= A′ [(B’ A) (B’ B)]


{ Distributive property of set:


(A B) (A C) = A (B C)}


= A′ [(A B’) Φ]


{ (B’ B) = Φ}


= A′ (A B’)


= (A’ A) (A’ B’)


{ Distributive property of set:


(A B) (A C) = A (B C)}


= Φ (A’ B’)


{ (A’ A) = Φ}


= (A’ B’)


= (A B)’


{ (A’ B’) = (A B)’}


A′ (A B) B′ = (A B)’


A contains all odd numbers and B contains all even numbers


Hence, A B = Φ


A′ (A B) B′ = {Φ}’


A′ (A B) B′ = N

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