Q51 of 58 Page 12

Fill in the blanks
For all sets A and B, A – (A ∩ B) is equal to ______________.

A ∩ B’

Given: A and B are two given sets

To find: A – (A ∩ B)

A – (A ∩ B)

= A ∩ (A ∩ B)’

{∵ A – B = A ∩ B’}

= A ∩ (A’ ∪ B’)

{∵ (A ∩ B)’ = A’ ∪ B’}

= (A ∩ A’) ∪ (A ∩ B’)

{∵ Distributive property of set:

(A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)}

= Φ ∪ (A ∩ B’)

{∵ A ∩ A’ = Φ}

= A ∩ B’

A – (A ∩ B) = A ∩ B’

Fill in the blanks

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______________.

Fill in the blanks

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then

(i) (B ∪ C)′ is ______________.

(ii)(C – A)′ is ______________.

Match the following sets for all sets A, B and C

State True or False for the following statements

If A is any set, then A ⊂ A

Fill in the blanksFor all sets A and B, A – (A ∩ B) is equal to ______________.