What is the nature of the set A = {x ∈ ℝ : |x - 4| + |x - 9| = 5}?
Answer and explanation
Correct answer: An infinite set (अपरिमित समुच्चय)
The expression |x - 4| + |x - 9| represents the sum of the distances from x to 4 and 9 on the number line. The distance between 4 and 9 is 5, so for every x in the closed interval [4, 9], the sum is exactly 5. Since an interval contains infinitely many real numbers, A is an infinite set.
Frequently asked questions
What is the correct answer to this question?
An infinite set (अपरिमित समुच्चय)
Why is this the correct answer?
The expression |x - 4| + |x - 9| represents the sum of the distances from x to 4 and 9 on the number line. The distance between 4 and 9 is 5, so for every x in the closed interval [4, 9], the sum is exactly 5. Since an interval contains infinitely many real numbers, A is an infinite set.
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.
