Question

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 1

(i) False As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6} ⇒ {2, 3, 4, 5} ∩ {3, 6} = {3} 

(ii) False As a ∈ {a, e, i, o, u}, a ∈ {a, b, c, d} ⇒ {a, e, i, o, u } ∩ {a, b, c, d} = {a} 

(iii) True As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ 

(iv) True As {2, 6, 10} ∩ {3, 7, 11} = Φ