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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.

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.

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