Question

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

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

Answer 1

Hint: In order to solve this question, we can approach from any column to get the correct answer, and therefore we will approach from the right column towards the left column. Also, we know that the set-builder form is used to get all the possible elements of the roster form. Now write all values obtained from RHS for each different option and compare them with the set present in the LHS.

Complete step-by-step answer:

In this question, we have matched the left column of the roster form with the same set on the right column described in the set builder form. So, we will start our approach from the right column to the left column and therefore let us consider each option of the right column one by one.
(a) \left\\{ x:x\in Z\text{ and }{{\text{x}}^{2}}<16 \right\\}
Here, we have been given that x follows a relation that is ${{x}^{2}}<16$ and a range of x is an integer, that is x is like 0, $\pm 1$, $\pm 2$ and so on. Therefore, according to the given conditions, we can say that the possible values of x are {– 3, – 2, – 1, 0, 1, 2, 3}. Or we can write it as option (a) right column matches with option (iii) of the left column.
(b) \left\\{ x:x\in N\text{ and }{{\text{x}}^{2}}=x \right\\}
Here, we have been given that x follows a relation that is ${{x}^{2}}=x$ and range of x is given as natural numbers and we know that natural numbers are {1, 2, 3, ….}, that is all non-negative integers other than 0. So, from the given conditions, we can say that the only possible value of x is {1}. Or we can write it as an option (b) of the right column matches with option (v) of the left column.
(c) \left\\{ x:x\in Z\text{ and }{{\text{x}}^{2}}=25 \right\\}
Here, we have been given that ${{x}^{2}}=25$ and x belongs to integers. So, we will consider all the possible values of x either positive or negative. So, from the given conditions, we can say that x can be possibly {– 5, 5}. And therefore, we can write option (c) of right column matches with option (i) of the left column.
(d) \left\\{ x:x\in N\text{ and x is a factor of 18} \right\\}
In this option, we have been given a relation for a that is x is a factor of 18 and $x\in N$ which means x belongs to natural numbers. Now, let us write the factors of 18, then we will get 1, 18, 2, 9, 3, and 6. So, we will get the possible value of x as {1, 2, 3, 6, 9, 18}, that is option (ii). Hence we can say that option (d) of the right column matches with option (ii) of the left column.
(e) {x : x is a letter in the word ‘PRINCIPAL’}
In this option, we have been given that x is a letter and at the same time we have been given that x is a letter of the word ‘PRINCIPAL’. So, we can write the possible value of x as {P, R, I, N, C, A, L}. Hence, we can say that option (e) of the right column matches with option (iv) of the left column.
Hence, we can conclude that (i) goes with (c), (ii) goes with (d), (iii) goes with (a), (iv) goes with (e) and (v) goes with (b).

Note: While solving this question, one can mistake only when we don’t know that N represents natural numbers that are {1, 2, 3, …..}, Z represents integers that is {0, $\pm 1$, $\pm 2$,….}. Also, we need to remember that natural numbers never include 0 in the range. The order of solving is not important here. We can try to eliminate the most obvious pairs first and then match the rest. The set (iv) can be matched with the set (e) only, so we can match it first. Also, next, we can match the set (i) with the set (c) and continue with rest.