Question

Match each of the sets on the left in the roster form with the same set on the right described in the set-builder form:
(i) {A,P,L,E} (i) {x : x+5=5, x ∈ z}
(ii) {5,-5} (ii) {x : x is a prime natural number and a divisor of 10}
(iii) {0} (iii) {x : x is a letter of the word “RAJASTHAN”}
(iv) {1, 2, 5, 10} (iv) {x : x is a natural and divisor of 10}
(v) {A, H, j, R, S, T, N} (v) {x : x² – 25 =0}
(vi) {2,5} (vi) {x : x is a letter of word “APPLE”}

Answer 1

(i) {A, P, L, E} ⇔ {x: x is a letter of word “APPLE”}

(ii) {5,-5} ⇔ {x: x² – 25 =0}

Here, the solution set of x² – 25 = 0 is x = ±5

(iii) {0} ⇔ {x: x+5=5, x ∈ z}

Since the solution set of x + 5 = 5 is x = 0.

(iv) {1, 2, 5, 10} ⇔ {x: x is a natural and divisor of 10}

Since, the natural numbers which are divisor of 10 are 1, 2, 5, 10.

(v) {A, H, j, R, S, T, N} ⇔ {x: x is a letter of the word “RAJASTHAN”}

Here, the distinct letters of word “RAJASTHAN” are A, H, j, R, S, T, N.

(vi) {2, 5} ⇔ {x: x is a prime natural number and a divisor of 10}

Since, the prime natural numbers which are divisor of 10 are 2, 5.