Question

5. Verify the following.
If A = {1,4,5), B = {3,4,9and C = {2, 3, 7} Then,
a) Is (A - B) = (B - A)?
b) Is (B-C)=(C-B)?​

Answer 1

Answer :

a). No

b). No

Note :

★ Difference of sets : The difference of two sets A and B in the order ( also called relative complement of B in A ) is the set of all those elements of A which are not the elements of B .

→ It is denoted by (A - B) .

Solution :

Here ,

The given sets are :

A = { 1 , 4 , 5 }

B = { 3 , 4 , 9 }

C = { 2 , 3 , 7 }

a). Is (A - B) = (B - A) ?

=> A - B = { 1 , 4 , 5 } - { 3 , 4 , 9 }

=> A - B = { 1 , 5 }

=> B - A = { 3 , 4 , 9 } - { 1 , 4 , 5 }

=> B - A = { 3 , 9 }

Clearly ,

(A - B) ≠ (B - A)

b). Is (B - C) = (C - B) ?

=> B - C = { 3 , 4 , 9 } - { 2 , 3 , 7 }

=> B - C = { 4 , 9 }

=> C - B = { 2 , 3 , 7 } - { 3 , 4 , 9 }

=> C - B = { 2 , 7 }

Clearly ,

(B - C) ≠ (C - B)