If A = {x : x ∈ N, 10 < x < 16} and B = {11, 12, 13, 14, 15}, which statement is correct?
Answer and explanation
Correct answer: A = B
The inequality 10 < x < 16 is strict at both ends. Among natural numbers, the values satisfying it are 11, 12, 13, 14, and 15. Thus A = {11, 12, 13, 14, 15}, which is exactly the set B. Neither 10 nor 16 is included because the inequalities are not ≤. Therefore A = B, so option A is correct; options B and C incorrectly claim proper inclusion, and option D is false.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The inequality 10 < x < 16 is strict at both ends. Among natural numbers, the values satisfying it are 11, 12, 13, 14, and 15. Thus A = {11, 12, 13, 14, 15}, which is exactly the set B. Neither 10 nor 16 is included because the inequalities are not ≤. Therefore A = B, so option A is correct; options B and C incorrectly claim proper inclusion, and option D is false.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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