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(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

Answer
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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.

Complete step-by-step answer:

A set is a collection of distinct objects, and these objects are called elements of the set. These elements can be anything: numbers, shapes, symbols, animals, colors, even other sets.

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: \[S=\left\{ 0,\,2,\,4,\,6,\,8,\,10 \right\}\]

Sets are unordered, which means that we can write their elements in any order in roster form.

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.

Hence option (a) only is the roster form of representation of sets.

Note: Knowing the definition of the roster form of representation of sets is important. We can make a mistake by thinking option c also as the answer because this expression is also enclosed by braces but here two pairs of parenthesis is also included and hence option (c) is not the answer.

Complete step-by-step answer:

A set is a collection of distinct objects, and these objects are called elements of the set. These elements can be anything: numbers, shapes, symbols, animals, colors, even other sets.

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: \[S=\left\{ 0,\,2,\,4,\,6,\,8,\,10 \right\}\]

Sets are unordered, which means that we can write their elements in any order in roster form.

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.

Hence option (a) only is the roster form of representation of sets.

Note: Knowing the definition of the roster form of representation of sets is important. We can make a mistake by thinking option c also as the answer because this expression is also enclosed by braces but here two pairs of parenthesis is also included and hence option (c) is not the answer.

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