Which statement is correct about A = {x ∈ ℝ : |x − 3| = −1}?
Answer and explanation
Correct answer: A is the empty set
For every real number x, the absolute value |x − 3| is non-negative, so it can be zero or positive but never −1. Consequently, the equation |x − 3| = −1 has no real solution. Since A consists of real numbers satisfying this impossible condition, it contains no elements. Therefore, A is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
A is the empty set
Why is this the correct answer?
For every real number x, the absolute value |x − 3| is non-negative, so it can be zero or positive but never −1. Consequently, the equation |x − 3| = −1 has no real solution. Since A consists of real numbers satisfying this impossible condition, it contains no elements. Therefore, A is the empty set, written as ∅.
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.
