How many elements are in H = {x : x ∈ N, 10 < x < 20, and x is even}?
Answer and explanation
Correct answer: 4
The inequalities are strict, so the endpoints 10 and 20 are not included. The natural numbers between them are 11, 12, 13, 14, 15, 16, 17, 18 and 19. Selecting only the even values leaves 12, 14, 16 and 18. Thus H has four elements, written n(H) = 4. Counting 10 or 20 would incorrectly treat < as ≤, and counting every integer would ignore the evenness condition.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The inequalities are strict, so the endpoints 10 and 20 are not included. The natural numbers between them are 11, 12, 13, 14, 15, 16, 17, 18 and 19. Selecting only the even values leaves 12, 14, 16 and 18. Thus H has four elements, written n(H) = 4. Counting 10 or 20 would incorrectly treat < as ≤, and counting every integer would ignore the evenness condition.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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