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 ______________.

(i) {1, 5, 9, 10} (ii) {1, 2, 3, 5, 6, 7, 9, 10}

Given: 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}

To find: (B ∪ C)′ and (C – A)′

Formula used:

The union of two sets is a set containing all elements that are in both sets.

For example: {1, 2, 3} ∪ {2, 4} = {1, 2, 3, 4}

The difference (subtraction) is defined as: The set A – B consists of elements that are in A but not in B.

For example: if A = {1, 2, 3} and B = {3, 5}, then A−B = {1, 2}

B = {2, 4, 6, 7} and C = {2, 3, 4, 8}

B ∪ C = {2, 3, 4, 6, 7, 8}

(B ∪ C)’ = U – (B ∪ C)

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

= {1, 5, 9, 10}

A = {1, 2, 3} and C = {2, 3, 4, 8}

C – A = {4, 8}

(C – A)’ = U – (C – A)

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

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