If C={x∈Z: -5<x≤3}, how many elements does C have?
Answer and explanation
Correct answer: 8
The set-builder condition restricts x to integers strictly greater than −5 and less than or equal to 3. Therefore, the eligible integers are −4, −3, −2, −1, 0, 1, 2, and 3. Counting this list gives 8 elements, so option B is correct. The endpoint −5 is excluded because the inequality is strict, while 3 is included because the inequality is inclusive. Zero must also be counted as an integer.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The set-builder condition restricts x to integers strictly greater than −5 and less than or equal to 3. Therefore, the eligible integers are −4, −3, −2, −1, 0, 1, 2, and 3. Counting this list gives 8 elements, so option B is correct. The endpoint −5 is excluded because the inequality is strict, while 3 is included because the inequality is inclusive. Zero must also be counted as an integer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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