Question

Write the following set in the roaster method:
A=\left\\{ x:x\text{ is a colour in the rainbow} \right\\}

Answer 1

Hint: In this question, as we know that there are 7 colours in the rainbow, so our set must have 7 elements. Now, from the given set builder we need to list all the 7 colours in the rainbow. Then using the form to be listed as x we need to group them accordingly and write as a roster form.

Complete step by step solution:
SET:
Set is a collection of well defined objects which are distinct from each other. Sets are usually denoted by capital letters A, B, C,.... and elements are usually denoted by small letters a, b, c,....
Methods of Describing a Set:
Roster/Listing Method/Tabular Form: In this method, a set is described by listing elements, separated by commas, within braces.
e.g. A=\left\\{ a,e,i,o,u \right\\}
Set Builder/Rule Method: In this method, we write down a property or rule which gives us all the elements of the set by that rule.
e.g. A=\left\\{ x:x\text{ is a vowel of English alphabets} \right\\}
Now, in this question given set is
A=\left\\{ x:x\text{ is a colour in the rainbow} \right\\}
Now, let us first list all the colours that are present in the rainbow which are
Violet, Indigo, Blue, Green, Yellow, Orange, Red
As we already know that in roster form to represent a particular set of curly braces and write the according elements inside the curly braces separated by brackets.
Now, the roster form of the set builder form of set given in the question is
A=\left\\{ \operatorname{Violet},Indigo,Blue,Green,Yellow,\operatorname{Orange},Red \right\\}
Note:
Instead of writing the colours with their complete names we can also represent them with their first letters and then list them accordingly in the roster form. Both methods are similar and can be followed.
It is important to note that in the roster form we should not forget the brackets after each of the elements inside the curly braces. Because forgetting commas does not give the roster form.