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’}



(i) {-5, 5}

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)



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