If A = (−∞, 4] and B = (1, ∞), what is A ∩ B?
Answer and explanation
Correct answer: (1, 4]
An intersection contains only the numbers common to both sets. Set A contains all numbers up to and including 4, while set B contains all numbers strictly greater than 1. A common number must therefore be greater than 1 and less than or equal to 4. The lower endpoint is open because 1 is excluded from B, and the upper endpoint is closed because 4 is included in A. Thus A ∩ B = (1, 4], so option A is correct.
Frequently asked questions
What is the correct answer to this question?
(1, 4]
Why is this the correct answer?
An intersection contains only the numbers common to both sets. Set A contains all numbers up to and including 4, while set B contains all numbers strictly greater than 1. A common number must therefore be greater than 1 and less than or equal to 4. The lower endpoint is open because 1 is excluded from B, and the upper endpoint is closed because 4 is included in A. Thus A ∩ B = (1, 4], so option A 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).
