Question

Match each of the sets on the left in the roster form with the same set on the right given in set builder form.

(i). \left\\{ 23,29 \right\\}	(a). \left\\{ x:x={{3}^{n}},n\in N\text{ }and\text{ }1\le n\le 5 \right\\}
(ii). \left\\{ B,E,T,R \right\\}	(b). \left\\{ x:x={{n}^{3}},n\in N\text{ }and\text{ }2\le n\le 6 \right\\}
(iii). \left\\{ 3,9,27,81,243 \right\\}	(c). $x:x$ is prime, 20$<$x$<$30
(iv). \left\\{ 8,27,64,125,216 \right\\}	(d). \left\\{ x:x\text{ }is\text{ }a\text{ }letter\text{ }of\text{ }word\text{ }'BETTER' \right\\}

Answer 1

Hint: To solve the given question, we can approach from any column to get the correct answer. So, 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.

Complete step-by-step answer:

In this question, we have to match the left column of roster form with the same set on the right column, which is described in set builder form. So, we will start our approach from the right column towards the left column. Therefore, let us consider each option on the right side one by one.
a. \left\\{ x:x={{3}^{n}},n\in N\text{ }and\text{ }1\le n\le 5 \right\\}
Here, we have been given that x follows a relation, that is $x={{3}^{n}}$ and the range of x belongs to natural numbers and that $1\le n\le 5$. So, when we consider ${{3}^{1}}$ we get 3. Similarly for the terms up to n = 5, we get, ${{3}^{2}}=9,{{3}^{3}}=27,{{3}^{4}}=81$ and ${{3}^{5}}=243$. Therefore, according to the given conditions, we can say that the possible values of x are \left\\{ 3,9,27,81,243 \right\\}. So, we can say that option (a) of the right column matches option (iii) of the left column.
b. \left\\{ x:x={{n}^{3}},n\in N\text{ }and\text{ }2\le n\le 6 \right\\}
Here we have been given that x follows a relation, that is $x={{n}^{3}}$ and the range of n is that n belongs to natural numbers and $2\le n\le 6$. So, when we consider n = 2, we get, ${{2}^{3}}=8$. Similarly for the values of n up to n = 6, we get the value of x as, ${{3}^{3}}=27,{{4}^{3}}=64,{{5}^{3}}=125$ and ${{6}^{3}}=216$. Therefore, according to the given conditions, we can say that the possible values of x are \left\\{ 8,27,64,125,216 \right\\}. So, we can say that option (b) of the right column matches option (iv) of the left column.
c. $x:x$ is prime, 20$<$x$<$30
Here we have been given that x follows a relation which is that, x is a prime number and the range of x is given in the question as $20 < x <30$. We know that prime numbers have only 2 factors, 1 and the number itself. So, the only possible numbers in the range from 20 to 30 are 23 and 29. Therefore, according to the given conditions, we can say that the possible values of x are \left\\{ 23,29 \right\\}. So, we can say that option (c) of the right column matches option (i) of the left column.
d. \left\\{ x:x\text{ }is\text{ }a\text{ }letter\text{ }of\text{ }word\text{ }'BETTER' \right\\}
In this option, we have been given a relation for x, that is, x is a letter and at the same time we have been given that x is a letter of the word, ‘BETTER’. So, from the given conditions, we get the possible value of x as, \left\\{ B,E,T,R \right\\} or we can say that option (d) of right column matches option (ii) of left column.
Hence, we can conclude that options (i) goes with (c), (ii) goes with (d), (iii) goes with (a) and (iv) goes with (b).

Note: While solving this question, one can make mistakes only when you do not know that N represents natural numbers, that is {1, 2, 3, ……} and keep in mind that natural numbers never include 0. Also, alternatively, we can approach this question from the left column to the right column too.