Let A = {x : x ∈ N and x < 10}, and let B be the set of one-digit natural numbers. Which statement is true?
Answer and explanation
Correct answer: A = B
The phrase x < 10 restricts x to the natural numbers less than 10. Under the convention N = {1, 2, 3, ...}, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}; these are exactly the one-digit natural numbers, so A = B. Even if a text includes 0 in N, both definitions include the same one-digit natural numbers, so their equality remains true. Option D is not universally correct because it depends on whether 0 is included in N.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The phrase x < 10 restricts x to the natural numbers less than 10. Under the convention N = {1, 2, 3, ...}, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}; these are exactly the one-digit natural numbers, so A = B. Even if a text includes 0 in N, both definitions include the same one-digit natural numbers, so their equality remains true. Option D is not universally correct because it depends on whether 0 is included in N.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
