If A = {x ∈ R : -2 < x ≤ 6}, B = {x ∈ R : 1 ≤ x < 8}, and C = {x ∈ R : 4 < x ≤ 10}, what is (A ∪ C) − B?
Answer and explanation
Correct answer: (-2,1) ∪ [8,10]
First combine A and C. Since A covers all real numbers greater than -2 up to 6, and C covers numbers greater than 4 up to 10, their union is (-2,10]. Now subtract B = [1,8), which removes every number from 1 inclusive to 8 exclusive. The part below 1 remains (-2,1), while 8 remains because it is not in B, giving [8,10]. Therefore, the answer is (-2,1) ∪ [8,10].
Frequently asked questions
What is the correct answer to this question?
(-2,1) ∪ [8,10]
Why is this the correct answer?
First combine A and C. Since A covers all real numbers greater than -2 up to 6, and C covers numbers greater than 4 up to 10, their union is (-2,10]. Now subtract B = [1,8), which removes every number from 1 inclusive to 8 exclusive. The part below 1 remains (-2,1), while 8 remains because it is not in B, giving [8,10]. Therefore, the answer is (-2,1) ∪ [8,10].
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
