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} $\cap$ {4, 5, 6} = {4}
Therefore, this pair of sets is not disjoint.

---

(ii){a, e, i, o, u} $\cap$ (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} $\cap$ {x: x is an odd integer} =$\phi$
Therefore, this pair of sets is disjoint.