If A = {x : x ∈ N and x ≤ 5} and B = {x : x ∈ N and x < 5}, which relation is correct?
Answer and explanation
Correct answer: B ⊂ A and B ≠ A
Taking N = {1, 2, 3, …}, the condition x ≤ 5 gives A = {1, 2, 3, 4, 5}, whereas x < 5 gives B = {1, 2, 3, 4}. Every element of B belongs to A, so B ⊆ A. Since 5 is in A but not in B, equality fails and B is a proper subset of A. Thus option B is correct; the sets are not disjoint and the inclusion direction is not reversed.
Frequently asked questions
What is the correct answer to this question?
B ⊂ A and B ≠ A
Why is this the correct answer?
Taking N = {1, 2, 3, …}, the condition x ≤ 5 gives A = {1, 2, 3, 4, 5}, whereas x < 5 gives B = {1, 2, 3, 4}. Every element of B belongs to A, so B ⊆ A. Since 5 is in A but not in B, equality fails and B is a proper subset of A. Thus option B is correct; the sets are not disjoint and the inclusion direction is not reversed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
