What is the correct statement about A = {x ∈ ℝ : 0 ≤ x ≤ 0}?
Answer and explanation
Correct answer: A = {0} and it is finite
The two inequalities must hold simultaneously: x must be at least 0 and at most 0. The only real number satisfying both conditions is x = 0. Therefore, A = {0}. This is a singleton set because it contains exactly one element, and every singleton set is finite. The use of inclusive signs is important; if the inequalities were strict, the result would instead be empty.
Frequently asked questions
What is the correct answer to this question?
A = {0} and it is finite
Why is this the correct answer?
The two inequalities must hold simultaneously: x must be at least 0 and at most 0. The only real number satisfying both conditions is x = 0. Therefore, A = {0}. This is a singleton set because it contains exactly one element, and every singleton set is finite. The use of inclusive signs is important; if the inequalities were strict, the result would instead be empty.
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.
