If A = {x ∈ Z : -4 ≤ x ≤ 6}, B = {x ∈ Z : x² ≤ 16}, and C = {x ∈ Z : 2 divides x}, what is (A ∩ B) − C?
Answer and explanation
Correct answer: {-3,-1,1,3}
The condition x² ≤ 16 gives -4 ≤ x ≤ 4 for integer x. This entire set lies inside A, because A contains every integer from -4 through 6. Hence A ∩ B = {-4,-3,-2,-1,0,1,2,3,4}. Set C contains the even integers, so removing C deletes -4,-2,0,2,4. The remaining odd integers are {-3,-1,1,3}, which is option A.
Frequently asked questions
What is the correct answer to this question?
{-3,-1,1,3}
Why is this the correct answer?
The condition x² ≤ 16 gives -4 ≤ x ≤ 4 for integer x. This entire set lies inside A, because A contains every integer from -4 through 6. Hence A ∩ B = {-4,-3,-2,-1,0,1,2,3,4}. Set C contains the even integers, so removing C deletes -4,-2,0,2,4. The remaining odd integers are {-3,-1,1,3}, which is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
