Question

"Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set (s) for all the three sets A, B, and C?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) Φ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}"

Answer 1

The universal sets that includes all the elements from sets A, B, and C is option (i) {0, 1, 2, 3, 4, 5, 6}.

Step-by-step explanation:

To identify the universal set for sets A, B, and C, we need to find a set that contains all the elements in A, B, and C. Looking at the given options:

1. (i) {0, 1, 2, 3, 4, 5, 6}
2. (ii) Φ
3. (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
4. (iv) {1, 2, 3, 4, 5, 6, 7, 8}

The universal set should include all elements from A, B, and C.

Option (i) {0, 1, 2, 3, 4, 5, 6} satisfies this condition because all the numbers in sets A, B, and C are included in this set.

Therefore, the correct option for the universal set is (i) {0, 1, 2, 3, 4, 5, 6}.