Question

Match each of the sets on the left described in the roster from with the same set on the right described in the set-builder from:

Column I	Column II
(i) {–5, 5}	(a) {x : x ϵ Z and x2 < 16}
(ii) {1, 2, 3, 6, 9, 18}	(b) {x : x ϵ N and x2 = x}
(iii) {–3, –2, –1, 0, 1, 2, 3}	(c) {x : x = ϵ Z and x2 =25}
(iv) {P, R, I, N, C, A, L}	(d) {x : x ϵ N and x is a factor of 18}
(v) {1}	(e) {x : x is a letter in the word ‘PRINCIPAL’}

Answer 1

It can be seen that if we take the square of -5 and 5, the result will be 25 

If x = -5, then (-5)² = 25 

If x = 5, then (5)² = 25 

and -5, 5 both are integers 

So, {x : x ∈Z and x² = 25} 

∴ (i) matches (c) 

(ii) {1, 2, 3, 6, 9, 18} 

Divisor of 18 are 

18 = 18 × 1 

18 = 9 × 2 

18 = 6 × 3 

1, 2, 3, 6, 9, 18 are divisors of 18 

So, {x : x ∈ N and x is a factor of 18} 

∴ (ii) matches (d) 

(iii) {–3, –2, –1, 0, 1, 2, 3} 

(-3)² = 9 < 16

(-2)² = 4 < 16 

(-1)² = 1 < 16 

(0)² = 0 < 16 

(1)² = 1 < 16 

(2)² = 4 < 16 

(3)² = 9 < 16 

All are the given elements are integers and satisfying x² < 16 So, 

(iii) matches (a) 

(iv) {P, R, I, N, C, A, L} 

There are 9 letters in the word PRINCIPAL out of which P and I are repeated. 

So, {x : x is a letter in the word ‘PRINCIPAL’} 

∴ (iv) matches (e) 

(v) {1} Since, 1 ∈ N and (1)² = 1 

So, {x : x ϵ N and x² = x} 

∴ (v) matches (b)