If A = {x ∈ ℝ : |x − 1| = 0}, what is the correct identification of A?
Answer and explanation
Correct answer: A = {1}, a singleton set
An absolute value is zero only when its inside expression is exactly zero. Thus |x − 1| = 0 implies x − 1 = 0, giving x = 1. Since the variable is restricted to real numbers, the solution set contains only 1. Consequently, A = {1}, which is a singleton set. The pair {−1, 1} would arise from an equation such as |x| = 1, not from |x − 1| = 0.
Frequently asked questions
What is the correct answer to this question?
A = {1}, a singleton set
Why is this the correct answer?
An absolute value is zero only when its inside expression is exactly zero. Thus |x − 1| = 0 implies x − 1 = 0, giving x = 1. Since the variable is restricted to real numbers, the solution set contains only 1. Consequently, A = {1}, which is a singleton set. The pair {−1, 1} would arise from an equation such as |x| = 1, not from |x − 1| = 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
