If A = [1, 5] and B = [3, 8], what is the interval A ∩ B?
Answer and explanation
Correct answer: [3, 5]
The intersection contains numbers that belong to both closed intervals. Its left endpoint is the larger of the two left endpoints, max(1, 3) = 3, and its right endpoint is the smaller of the two right endpoints, min(5, 8) = 5. Since both original intervals include their endpoints, the answer is the closed interval [3, 5]. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
[3, 5]
Why is this the correct answer?
The intersection contains numbers that belong to both closed intervals. Its left endpoint is the larger of the two left endpoints, max(1, 3) = 3, and its right endpoint is the smaller of the two right endpoints, min(5, 8) = 5. Since both original intervals include their endpoints, the answer is the closed interval [3, 5]. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
