If A = (-∞, 3] and B = [0, 5), what is A ∩ B?
Answer and explanation
Correct answer: [0,3]
The interval A contains every real number less than or equal to 3. The interval B contains every real number from 0 inclusive up to 5 exclusive. Their common part therefore begins at 0, which is included in both intervals, and ends at 3, which is also included in both. Thus A ∩ B = [0,3]. The endpoint 5 is irrelevant because it is not common to both intervals. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
[0,3]
Why is this the correct answer?
The interval A contains every real number less than or equal to 3. The interval B contains every real number from 0 inclusive up to 5 exclusive. Their common part therefore begins at 0, which is included in both intervals, and ends at 3, which is also included in both. Thus A ∩ B = [0,3]. The endpoint 5 is irrelevant because it is not common to both intervals. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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