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 insufficientD. None of these

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.

The given set is ${\text{F = }}\left\{ {{\text{I,}}\;{\text{N, D, A}}} \right\}$
Given that the set ${\text{F}}$ contains the letters ${\text{I,}}\;{\text{N, D, A}}$.
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’${\text{\} }}$
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.