Question

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

(i) \[\{ 1,2,3,6\} \]	(a) {x: x is a prime number and a divisor of 6}
(ii) \[\{ 2,3\} \]	(b) {x: x is an odd natural number less than 10}
(iii) \[\{ M,A,T,H,E,I,C,S\} \]	(c) { x: x is natural number and divisor of 6}
(iv) \[\{ 1,3,5,7,9\} \]	(d) { x: x is a letter of the word MATHEMATICS}

Answer 1

Hint: Firstly we convert the set given in set-builder form to roaster form, and then we match the corresponding set-builder form to the roaster form given on the right side.

Complete step by step solution: Firstly we have,
a) {x: x is a prime number and a divisor of 6}
So, we have that 2 and 3 are prime numbers and they are a divisor of 6, so our set in roster form is \[\{ 2,3\} \]

Hence, we have that a) matches to ii).

b) {x: x is an odd natural number less than 10}
We, have 1,3,5,7,9 as odd natural numbers which are less than 10, so our set in roster form will be \[\{ 1,3,5,7,9\} \].

Hence, we have that b) matches to iv).

c) { x: x is natural number and divisor of 6}
So, 1,2,3,6 are the natural numbers and also divisor of 6, so our set in roster form will be, \[\{ 1,2,3,6\} \].

Hence, we have c) matches to i).

d) { x: x is a letter of the word MATHEMATICS}
Here, the letter of the word MATHEMATICS are M,A,T,H,E,I,C,S , So our set in roster form will be \[\{ M,A,T,H,E,I,C,S\} \].

Hence, we have d) matches to iii).

Note: Note: For a set to be properly defined it has to a well-defined collection of distinct objects. So every set we check out has a collection of distinct objects. In the set, \[\{ M, A, T, H, E, I, C, S \} \] we have, 8 elements whereas the word MATHEMATICS has 10 letters because few letters are repeating but as they are identical, we don’t consider them again in the set.