Which option gives the correct roster form of U = {x ∈ Z : x² − 1 = 0}?
Answer and explanation
Correct answer: English: U = {-1, 1} | हिन्दी: U = {-1, 1}
To determine the members of U, solve the defining equation x² − 1 = 0. Using the difference of squares, x² − 1 = (x − 1)(x + 1). Hence either x − 1 = 0, giving x = 1, or x + 1 = 0, giving x = −1. Both values belong to the integers, so both must be included. Therefore U = {-1, 1}, making option A correct. Zero does not satisfy the equation because 0² − 1 = −1.
Frequently asked questions
What is the correct answer to this question?
English: U = {-1, 1} | हिन्दी: U = {-1, 1}
Why is this the correct answer?
To determine the members of U, solve the defining equation x² − 1 = 0. Using the difference of squares, x² − 1 = (x − 1)(x + 1). Hence either x − 1 = 0, giving x = 1, or x + 1 = 0, giving x = −1. Both values belong to the integers, so both must be included. Therefore U = {-1, 1}, making option A correct. Zero does not satisfy the equation because 0² − 1 = −1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
