If A = {x : x ∈ N and x ≤ 6} and B = {x : x is a positive divisor of 6}, what is the relation between A and B?
Answer and explanation
Correct answer: B is a proper subset of A.
Assuming N denotes the positive natural numbers, A = {1, 2, 3, 4, 5, 6}. The positive divisors of 6 are B = {1, 2, 3, 6}. Every element of B is in A, so B is a subset of A. However, A also contains 4 and 5, which are not in B. Thus B is not equal to A; it is a proper subset of A, making option B correct.
Frequently asked questions
What is the correct answer to this question?
B is a proper subset of A.
Why is this the correct answer?
Assuming N denotes the positive natural numbers, A = {1, 2, 3, 4, 5, 6}. The positive divisors of 6 are B = {1, 2, 3, 6}. Every element of B is in A, so B is a subset of A. However, A also contains 4 and 5, which are not in B. Thus B is not equal to A; it is a proper subset of A, making option B correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
