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.

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(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.

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(iii) {x: x is an even integer} \(\cap\) {x: x is an odd integer} =\(\phi\)
Therefore, this pair of sets is disjoint.