Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
$(i)$ $\{1, 2, 3, 6\}$ $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$ $(ii)$ $\{2, 3\}$ $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$ $(iii)$ $\{M, A, T, H, E, I, C, S\}$ $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$ $(iv)$ $\{1, 3, 5, 7, 9\}$ $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$
| $(i)$ $\{1, 2, 3, 6\}$ | $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$ |
| $(ii)$ $\{2, 3\}$ | $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$ |
| $(iii)$ $\{M, A, T, H, E, I, C, S\}$ | $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$ |
| $(iv)$ $\{1, 3, 5, 7, 9\}$ | $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$ |
(A) $(i)$ All the elements of this set are natural numbers as well as the divisors of $6$. Therefore,$(i)$ matches with $(c)$.
$(ii)$ It can be seen that $2$ and $3$ are prime numbers. They are also the divisors of $6$. Therefore,$(ii)$ matches with $(a)$.
$(iii)$ All the elements of this set are letters of the word $MATHEMATICS$. Therefore,$(iii)$ matches with $(d)$.
$(iv)$ All the elements of this set are odd natural numbers less than $10$. Therefore,$(iv)$ matches with $(b)$.
$(ii)$ It can be seen that $2$ and $3$ are prime numbers. They are also the divisors of $6$. Therefore,$(ii)$ matches with $(a)$.
$(iii)$ All the elements of this set are letters of the word $MATHEMATICS$. Therefore,$(iii)$ matches with $(d)$.
$(iv)$ All the elements of this set are odd natural numbers less than $10$. Therefore,$(iv)$ matches with $(b)$.
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