Question

# Write the set builder form $A = \{ - 1,1\} $A = \{ x:x{\text{ is a real number}}\}$A = \{ x:x{\text{ is an integer}}\} $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\}$A = \{ x:x{\text{ is a root of the equation }}{x^2} + 1 = 0\}$

Hint: Here set builder form is a mathematical notation for describing a set by enumerating its
elements or stating the properties that its members must satisfy.
Given set builder form of $A = \{ - 1,1\}$
Clearly, we know that $- 1$ and $1$are the roots of the equation ${x^2} = 1$
So, the set builder form of the equation ${x^2} = 1$ is $\{ - 1,1\}$ which is equal to the set builder
form of $A = \{ - 1,1\}$.

Hence given set in set builder form can be written as,
$A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\}$
Thus, the set builder form of $A = \{ - 1,1\}$ is $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\}$
Therefore, option $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\}$

Note: In this problem the representation is not unique, but among the given options only option $A = \{ x:x{\text{ is a root of the equation }}{x^2} = 1\}$ is satisfying the condition.