Question

1.Let U={1,2,3,4,5,6,7,8,9), B = {1,3,5,7}
(a) Find AUB
(b) Find A’,B' and hence show that (AUB)' = A'nB' ​

Answer 1

SOLUTION

GIVEN

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

TO DETERMINE

(a) A ∪ B

(b) A' , B'

To show : ( A ∪ B) ' = A' ∩ B'

EVALUATION

Here the given sets are

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

A = {1,2,4,7}

B = {1,3,5,7}

(a) A ∪ B

= { x : x ∈ A ∨ x ∈ B }

= { 1 , 2 , 3 , 4 , 5 , 7 }

(b)

A' = { x ∈ U : x ∉ A } = { 3, 5, 6 , 8, 9 }

B' = { x ∈ U : x ∉ B } = { 2 ,4, 6, 8 ,9 }

PROOF :

LHS = ( A ∪ B) ' = { 6 , 8 , 9 }

RHS = A' ∩ B'

= { 3, 5, 6 , 8, 9 } ∩ { 2 ,4, 6, 8 ,9 }

= { 6 , 8 , 9 }

∴ ( A ∪ B) ' = A' ∩ B'

Hence proved

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