Question

A =(x is a number bigger than 4
and smaller than 8)
B = (x:x is a positive number
smaller than 7)
Find AUB, AnB ,A-B,B-A ?​

Answer 1

Answer:

a={5,6,7}

then b={1,2,3,4,5,6}

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

=1,2,3,4,5,6,7 (all the elements in both sets)

AΠB={5,6,7}Π{1,2,3,4,5,6}

=5,6 (common elements in both sets)

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

=7 (the element which belong to set A but not B) B-A ={1,2,3,4,5,6,7}-{5,6,7}

=1,2,3,4 (the sets which belong to set B but not A)

I hope it is helpful for you...

thank you!!!

Answer 2

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 : AUB, A∩B ,A-B,B-A

Also 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

A-B  = { 7}

B - A = { 1 , 2 , 3 , 4 }

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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