Question

Write the following set in the set-builder form.
\[{\text{F = }}\left\{ {{\text{I,}}\;{\text{N, D, A}}} \right\}\]
A. \[{\text{F = \{ x|x}}\] is a letter in the word ‘INDIA’\[{\text{\} }}\]
B. \[{\text{F = \{ x|x}}\] is a letter in the word ‘IND’\[{\text{\} }}\]
C. Data insufficient
D. None of these

Answer 1

Hint: In this problem the given is in the roster form. We have to find the set-builder form of the given set.
Set-builder form is a form for describing a set by indicating the properties that its members must satisfy.
That is, A set is a collection of things (usually numbers). We can build a set by describing what is in it. Here is a simple example of set builder notation:
\[\left\{ {x|x > 0} \right\}\]
The representation of the symbols are following,
\[\{ \] the set of \[x\] : for all \[x\] : such that \[x > 0\] : \[x\] is greater than zero
So it says “The set of all \[x\]’s, such that \[x\] is greater than \[0\]”
Similarly we need to write the set builder form of the given set which describes what is in it.

Complete step-by-step answer:
We know, to express the set in Set-builder Form actual elements of the set are not listed but a rule or a statement or a formula in the briefest possible way
The given set is \[{\text{F = }}\left\{ {{\text{I,}}\;{\text{N, D, A}}} \right\}\]
We need to write the set builder form of the given set.
We know that set builder form describes what is in it.
Given that the set \[{\text{F}}\] contains the letters \[{\text{I,}}\;{\text{N, D, A}}\].
Thus we can clearly see that these are the letters of INDIA.
Therefore we get that, \[{\text{F}}\] is a set of all \[x\]’s ,such that , \[x\] is a letter in the word .
So, \[{\text{F = \{ x|x}}\] is a letter in the word ‘INDIA’\[{\text{\} }}\]

So, the correct answer is “Option A”.

Note: Sets, in mathematics, are an organized collection of objects and can be represented in roster form. Usually, sets are represented in curly braces \[\{ \} \], for example, \[A = \left\{ {1,\;2,\;3,\;4} \right\}\] is a set. In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.