Question

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

Answer 1

We have to match given roster form with the set builder form.

$\left(i\right)$ Given set is $\{1,2,3,6\}$
In the above set, the elements are natural numbers as well as divisors of $6$.
∴ $\left(i\right)$ Matches with $\left(c\right)$.

$\left(ii\right)$ Given set is $\{2,3\}$
In the above set, 2 and 3 are prime numbers which are also divisors of $6$.
∴ $\left(ii\right)$ Matches with $\left(a\right)$.

$\left(iii\right)$ Given set is $\left\{M,A,T,H,E,I,C,S\right\}$
In the above set, the elements are the letters of the word $MATHEMATICS$.
∴ $\left(iii\right)$ Matches with $\left(d\right)$.

$\left(iv\right)$ Given set is $\{1,3,5,7,9\}$
In the above set, the elements are odd natural numbers which are less than $10$.
∴ $\left(iv\right)$ Matches with $\left(b\right)$.

Final Answer: $\left(i\right)$ matches with $\left(c\right)$, $\left(ii\right)$ matches with $\left(a\right)$, $\left(iii\right)$ matches with $\left(d\right)$, $\left(iv\right)$ matches with $\left(b\right)$.