Question

If U = {x : x ∈ N, x ≤ 10}, A = {2,3,4,8,10} and B = {1,2,5,8,10}, then verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Answer 1

Given:
AUB = { 1, 2, 3, 4, 5, 8, 10}
AnB = { 2, 8, 10}

Now ,
n(A) = 5
n(B) = 5
n(AUB) = 7
n(AnB) = 3

n(A) + n(B) - n (AnB)

= 5 + 5 - 3

= 7

= n(AUB)

Hence verified

Answer 2

Solution :

i ) U = { x:x € N , x ≤ 10 }

U = { 1,2,3,4,5,6,7,8,9,10 }

n( U ) = 10 ,

ii ) A = { 2,3,4,8,10}

n(A) = 5 ,

iii ) B = { 1,2,5,8,10 }

n( B ) = 5 ,

iv )AUB ={ 2,3,4,8,10}U{1,2,5,8,10}

= { 1,2,3,4,5,8,10}

n(AUB) = 7 ,

v )A intersection B

= {2,3,4,8,10} intersection {1,2,5,8,10}

= { 2,8,10}

n( A intersection B ) = 3

Now ,

vi )RHS

= n(A)+n(B) - n(A intersection B)

= 5 + 5 - 3

= 7

= n( AUB )

= RHS

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