Question

4. A = {x : x is a number bigger than 4 and smaller than 8)
B = {x: x is a positive number smaller than 7}
Verify n(AUB) + n(
AB) = n(A) + n(B)


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Answer 1

Given  :  A = {x : x is a number bigger than 4 and smaller than 8)

B = {x: x is a positive number smaller than 7}

To find : Verify that

n( A U B ) + n( A ∩ B ) = n(A) + n(B)

Solution:

A = {x : x is a number bigger than 4 and smaller than 8)

4 < x  < 8

=> A = { 5 ,  6 ,  7 }

n(A) = 3

B = {x: x is a positive number smaller than 7}

=> B = { 1 , 2 , 3 , 4 , 5 ,  6 }

n(B)  = 6

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

=>n( A U B )  = 7

A ∩ B  = { 5 , 6}

n( A ∩ B ) = 2

n( A U B )  +  n( A ∩ B )  = 7 + 2 = 9

n(A) + n(B)  = 3 + 6  = 9

9 = 9

Hence n( A U B ) + n( A ∩ B ) = n(A) + n(B)

Verified

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