What is T={x:x∈Z, -8<x≤0, and x is odd}?
Answer and explanation
Correct answer: T={-7,-5,-3,-1}
The governing ideas are interval notation and parity of integers. First, -8<x≤0 gives the integers -7,-6,-5,-4,-3,-2,-1,0. From these, the odd integers are -7,-5,-3, and -1. The endpoint -8 is excluded because the inequality is strict, and 0 is even, so it is excluded by the oddness condition. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
T={-7,-5,-3,-1}
Why is this the correct answer?
The governing ideas are interval notation and parity of integers. First, -8<x≤0 gives the integers -7,-6,-5,-4,-3,-2,-1,0. From these, the odd integers are -7,-5,-3, and -1. The endpoint -8 is excluded because the inequality is strict, and 0 is even, so it is excluded by the oddness condition. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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