Question

# Identify the Roster form of representation of sets?(a) $\left\{ 1,\,2,\,3 \right\}$(b) $\left\{ (x,\,y):x\in N,\,x<2,\,y=x-1 \right\}$(c) $\left\{ (1,\,2),\,(2,\,3) \right\}$(d) None of these

Hint: In roster form of representation, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces.

Now to write a set in roster form, all we have to do is list each element of the set, separated by commas, within a pair of curly braces. The set of even numbers between 0 and 10 is represented by set S in roster form: $S=\left\{ 0,\,2,\,4,\,6,\,8,\,10 \right\}$
Let’s start with option (a) $\left\{ 1,\,2,\,3 \right\}$, where the elements are separated by commas and are enclosed within braces. So yes option (a) is the roster form of representation of sets.
Now checking option (b) $\left\{ (x,\,y):x\in N,\,x<2,\,y=x-1 \right\}$, here the elements x, y are separated by commas and are enclosed within braces, rest of the terms are preconditions for x and y but there is a colon which is an important characteristic of set builder form. So option (b) is not the roster form of representation of sets because it is in set builder form.
Now checking option (c) $\left\{ (1,\,2),\,(2,\,3) \right\}$, here the elements are enclosed by separate parenthesis and there is a comma between these. So option (c) is not the roster form of representation of sets.