If A = {a,b,c,d,e}, B = {b,d,f,g}, and C = {a,d,g,h}, what is (A ∩ C) ∪ (B \ A)?
Answer and explanation
Correct answer: {a,d,f,g}
First calculate the intersection A ∩ C. The elements common to A and C are a and d, so A ∩ C = {a,d}. Next calculate B \ A, which contains elements present in B but absent from A. Since b and d are in A, they are removed, leaving {f,g}. Taking the union gives {a,d} ∪ {f,g} = {a,d,f,g}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{a,d,f,g}
Why is this the correct answer?
First calculate the intersection A ∩ C. The elements common to A and C are a and d, so A ∩ C = {a,d}. Next calculate B \ A, which contains elements present in B but absent from A. Since b and d are in A, they are removed, leaving {f,g}. Taking the union gives {a,d} ∪ {f,g} = {a,d,f,g}. Therefore, 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).
