If A = {x : x ∈ ℕ, x ≤ 5} and B = {1, 2, 3, 4, 5, 6, 7}, which statement is correct?
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Answer and explanation
Correct answer: A ⊆ B; A is a subset of B
Assuming the school convention ℕ = {1, 2, 3, ...}, the condition x ≤ 5 gives A = {1, 2, 3, 4, 5}. Every element of A occurs in B, so A ⊆ B. The sets are not equal because B also contains 6 and 7. Moreover, 7 does not satisfy x ≤ 5, so 7 ∉ A. Thus A is the only correct statement.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B; A is a subset of B
Why is this the correct answer?
Assuming the school convention ℕ = {1, 2, 3, ...}, the condition x ≤ 5 gives A = {1, 2, 3, 4, 5}. Every element of A occurs in B, so A ⊆ B. The sets are not equal because B also contains 6 and 7. Moreover, 7 does not satisfy x ≤ 5, so 7 ∉ A. Thus A is the only correct statement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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