State whether each of the following statement is true or false. Justify your answer.

State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u } and {a, b, c, d} are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
Answer
(i) False
2, 3, 4, 5} ∩ {3, 6} = {3}
Intersection of set {2, 3, 4, 5} and {3, 6} is not equal to Φ.
So that {2, 3, 4, 5} and {3, 6} are not disjoint sets.
(ii) False
{a, e, i, o, u } ∩ {a, b, c, d} = {a}
Intersection of set {a, e, i, o, u } and {a, b, c, d} is not equal to Φ.
So that {a, e, i, o, u } and {a, b, c, d} are not disjoint sets.
(iii) True
{2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ
Intersection of set {2, 6, 10, 14} and {3, 7, 11, 15} is not equal to Φ.
So that {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) True
{2, 6, 10} ∩ {3, 7, 11} = Φ
Intersection of set {2, 6, 10} and {3, 7, 11} is not equal to Φ.
So that {2, 6, 10} and {3, 7, 11} are disjoint sets.