What type of set is A = {x ∈ R : |x − 2| + |x − 5| = 2}?
Answer and explanation
Correct answer: Empty set
The expression |x − 2| + |x − 5| represents the sum of the distances from x to 2 and 5 on the real number line. By the triangle inequality, this sum is always at least the distance between 2 and 5, which is 3. Since the question requires the sum to equal 2, no real number x can satisfy it. Hence A is the empty set.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The expression |x − 2| + |x − 5| represents the sum of the distances from x to 2 and 5 on the real number line. By the triangle inequality, this sum is always at least the distance between 2 and 5, which is 3. Since the question requires the sum to equal 2, no real number x can satisfy it. Hence A is the empty 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.
