If U = {x : x ∈ ℤ, −2 ≤ x ≤ 2}, how many elements does U have?
Answer and explanation
Correct answer: 5
Because x is an integer and both inequalities are inclusive, list every integer from −2 through 2: U = {−2, −1, 0, 1, 2}. This gives five distinct elements, so |U| = 5. The count can also be found by upper bound minus lower bound plus one: 2 − (−2) + 1 = 5. Excluding an endpoint would produce four, but the ≤ signs include both endpoints.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Because x is an integer and both inequalities are inclusive, list every integer from −2 through 2: U = {−2, −1, 0, 1, 2}. This gives five distinct elements, so |U| = 5. The count can also be found by upper bound minus lower bound plus one: 2 − (−2) + 1 = 5. Excluding an endpoint would produce four, but the ≤ signs include both endpoints.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
