If V = {x ∈ ℤ : -2 ≤ x < 3}, what is n(V)?
Answer and explanation
Correct answer: 5
Because x belongs to the integers, we list only whole-number values, not decimals or fractions. The inequality -2 ≤ x includes -2, while x < 3 excludes 3. Thus the elements are V = {-2, -1, 0, 1, 2}. Counting them gives five elements, so the cardinality of the set is n(V) = 5. The endpoint symbols are essential: the left endpoint is included because of ≤, and the right endpoint is excluded because of <.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Because x belongs to the integers, we list only whole-number values, not decimals or fractions. The inequality -2 ≤ x includes -2, while x < 3 excludes 3. Thus the elements are V = {-2, -1, 0, 1, 2}. Counting them gives five elements, so the cardinality of the set is n(V) = 5. The endpoint symbols are essential: the left endpoint is included because of ≤, and the right endpoint is excluded because of <.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
