Question

Which of the following pairs of sets are disjoint 

(i) {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6} 

(ii) {a, e, i, o, u} and {c, d, e, f} 

(iii) {x: x is an even integer} and {x: x is an odd integer} 

Answer 1

(i) {1, 2, 3, 4} {x: x is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6}

Now, {1, 2, 3, 4} ∩ {4, 5, 6} = {4}

Therefore, this pair of sets is not disjoint.

(ii) {a, e, i, o, u} ∩ (c, d, e, f} = {e} Therefore, {a, e, i, o, u} and (c, d, e, f} are not disjoint.

(iii) {x: x is an even integer} ∩ {x: x is an odd integer} = Φ

Therefore, this pair of sets is disjoint.