Question

Which of the following pairs of sets are disjoint?

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

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

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

Answer 1

(i) Let A = {1, 2, 3, 4}

and B = {x : x is a natural number and 4 $\le x\le 6$}

= {4, 5, 6}

$\therefore A\cap B$ = {1, 2, 3, 4} $\cap$ {4, 5, 6}

= {4}

Hence A and B are not disjoint.

(ii) Let A = {a, e, i, o, u}

and B = {b, c, d, f}

$\therefore A\cap B=\Phi$

Hence A and B are disjoint.

(iii) Let A = {x : x is an even integer}

and B = {x : x is an odd integer}

$\therefore A\cap B=\Phi$

Hence A and B are disjoint.