Question

In the following, state whether A = B or not :

(i) A = {a, b, c, d} B = {d, c, b, a}

(ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18}

(iii) A = {2, 4, 6, 8, 10} B = {x : x is a positive even integer and $x\le 10$

(iv) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, ...........}

Answer 1

(i) A = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not change a set.

$\therefore$ A = B = {a, b, c, d}.

(ii) A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because $12\in A,12\notin B$ and $18\in B,18\notin A.$

(iii) A = {2, 4, 6, 8, 10} and B = {x : x is a positive even integer and $x\le 10$} which can be written in roster form as B = {2, 4, 6, 8 10} are equal sets.

$\therefore$ A = B = {2, 4, 6, 8, 10}.

(iv) A = {x : x is a multiple of 10} can be written in roster form as A = {10, 20, 30, 40, ...........} and B = {10, 15, 20, 25, 30, ..................} are not equal sets because $15\in B,15\notin A.$