Question

Find the intersection of each of the following pairs of sets :

(i) X = {1, 3, 5} and Y = {1, 2, 3}

(ii) A = {a, e, i, o, u} and B = {a, b, c}

(iii) A = {x : x is a natural number and multiple of 3} and B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 < x $\le$ 6} and B = {x : is a natural number and 6 < x < 10}

(v) A = {1, 2, 3} and $B=\Phi$

Answer 1

(i) Here X = {1, 3, 5} and Y = {1, 2, 3}

$\therefore X\cap Y$ = {1, 3}

(ii) Here A = {a, e, i, o, u} and B = {a, b, c}

$\therefore A\cap B$ = {a}

(iii) Here A = {x : x is a natural number and multiple of 3}

= {3, 6, 9, 12, .......} and

B = {x : x is a natural number less than 6}

= {1, 2, 3, 4, 5}

$\therefore A\cap B$ = {3}

(iv) Here A = {x : x is a natural number and 1 < x $\le$ 6}

= {2, 3, 4, 5, 6}

and B = {x : x is a natural number and 6 < x < 10}

= {7, 8, 9}

$\therefore A\cap B=\Phi$

(v) Here A = {1, 2, 3} and $B=\Phi$

$\therefore A\cap B=\Phi$