Question

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of

 the following may be considered as universals 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

(i) It can be seen that A ⊂ {0, 1, 2, 3, 4, 5, 6} B ⊂ {0, 1, 2, 3, 4, 5, 6} 

However, C ⊄ {0, 1, 2, 3, 4, 5, 6} 

Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C. 

(ii) A ⊄ Φ, B ⊄ Φ, C ⊄ Φ Therefore, Φ cannot be the universal set for the sets A, B, and C. 

(iii) A ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} C ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.

(iv) A ⊂ {1, 2, 3, 4, 5, 6, 7, 8} B ⊂ {1, 2, 3, 4, 5, 6, 7, 8} However, C ⊄ {1, 2, 3, 4, 5, 6, 7, 8} Therefore, the set {1, 2, 3, 4, 5, 6, 7, 8} cannot be the universal set for the sets A, B, and C.