Given that = {x: -2 < x $\leq$ 9}, where x is an integer what is n(T)?

Analyze the question: The set is written as {x: -2 < x ≤ 9}, where x is an integer. (The set name seems to have been lost in the question, but it's T.) We need n(T), the number of elements in the set.

Concept: n(T) means the number of elements in T. Pay attention to the inequality signs:

• -2 < x means -2 is not included.
• x ≤ 9 means 9 is included.

Solution:

List the integers: -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Count them:

• Negative: -1 → 1 element
• Zero: 0 → 1 element
• Positive: 1 to 9 → 9 elements

Total = 1 + 1 + 9 = 11

Check with a formula: for integers with a < x ≤ b, the count is b − a = 9 − (−2) = 11. ✔

Answer: n(T) = 11, which is option C.

Tip: Watch out for the signs. When the lower limit is "<" (excluded) and the upper limit is "≤" (included), the count is simply upper − lower. If both ends were included, you would add 1. Also never forget that 0 counts as an element when the range crosses from negative to positive numbers.