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Question: Write the set builder form \(A = \\{ - 1,1\\} \) \(A = \\{ x:x{\text{ is a real number}}\\} \) \...

Write the set builder form A=−1,1A = \\{ - 1,1\\}
A=x:x is a real numberA = \\{ x:x{\text{ is a real number}}\\}
A=x:x is an integerA = \\{ x:x{\text{ is an integer}}\\}
A=x:x is a root of the equation x2=1A = \\{ x:x{\text{ is a root of the equation }}{x^2} = 1\\}
A=x:x is a root of the equation x2+1=0A = \\{ x:x{\text{ is a root of the equation }}{x^2} + 1 = 0\\}

Explanation

Solution

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=−1,1A = \\{ - 1,1\\}
Clearly, we know that −1 - 1 and 11are the roots of the equation x2=1{x^2} = 1
So, the set builder form of the equation x2=1{x^2} = 1 is −1,1\\{ - 1,1\\} which is equal to the set builder
form of A=−1,1A = \\{ - 1,1\\} .

Hence given set in set builder form can be written as,
A=x:x is a root of the equation x2=1A = \\{ x:x{\text{ is a root of the equation }}{x^2} = 1\\}
Thus, the set builder form of A=−1,1A = \\{ - 1,1\\} is A=x:x is a root of the equation x2=1A = \\{ x:x{\text{ is a root of the equation }}{x^2} = 1\\}
Therefore, option A=x:x is a root of the equation x2=1A = \\{ 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 is a root of the equation x2=1A = \\{ x:x{\text{ is a root of the equation }}{x^2} = 1\\} is satisfying the condition.