Question

Find the union 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 $\cup$ Y = {1, 2, 3, 5}

(ii) Here A = {1, e, i, o, u} and B = {a, b, c}

$\therefore$ $A\cup B$ = {a, b, c, e, i, o, u}

(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}

$\therefore A\cup B$ = {1, 2, 3, 4, 5, 6, 9, 12, 15, ......}

(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}

$\therefore A\cup B$ = {2, 3, 4, 5, 6, 7, 8, 9}

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

$\therefore A\cup B$ = {1, 2, 3}