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) { $x:x+5=5,xϵZ$}

(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 number and divisor of 10}

(v) {A, H, J, R, S T, N} (v) {$x:x^2-25=0$}

(vi) {2, 5} (vi) {x : X is a letter of the word "APPLE"}

Answer 1

(i) {A, P, L, E} $\leftrightarrow$ {x : x is a letter of the word "APPLE"}

(ii) The solution set of $x^2-25=0i.e.x=\pm 5$

Hence, {-5, 5} $\leftrightarrow$ {$x:x^2-25=0$}

(iii) The solution set of x + 5 = 5 i.e., x = 0

Hence, {0} $\leftrightarrow$ {$x:x+5=5,xϵZ$ }

(iv) The natural numbers which are divisor of 10 are 1, 2, 5, 10

Hence , {1,2,5,10} $\leftrightarrow$ {x : x is a natural number and divisor of 10 }

(v) The distinct letters of the word "RAJASTHAN" are A, H, J, R, S, T, H

Hence, {A, H, J, R, S, T, N} $\leftrightarrow$ {x : x is a letter of the word "RAJASTHAN" }

(vi) The prime natural numbers which are divisor of 10 are 2, 5

Hence , {2, 5} $\leftrightarrow$ {x : x is a prime natural number and a divisor of 10}