Q. 4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that

(i) (A \cup B)′ = A′ \cap B′

(ii) (A \cap B)′ = A′ \cup B′

Answers (1)

U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}

(i) (A \cup B)′ = A′ \cap B′

L.H.S = (A \cup B)′ = U - (A \cup B) = {1,9}

R.H.S =  A′ \cap B′ = {1,3,5,7,9} \cap {1,4,6,8,9} = {1,9}

L.H.S = R.H.S

Hence,the statement is true.

(ii) (A \cap B)′ = A′ \cup B′ 

 L.H.S = U - (A \cap B) ={1,3,4,5,6,7,8,9}

 R.H.S =  A′ \cup B′ = {1,3,5,7,9} \cup {1,4,6,8,9} = {1,3,4,5,6,7,8,9}

  L.H.S = R.H.S

Hence,the statement is true.

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