If \(A=\{1,3,5,7,9\}\), \(B=\{0,3,6,9\}\), and \(C=\{3,4,5,9\}\), what is \(A\cap(B\cup C)\)?
Answer and explanation
Correct answer: \(\{3,5,9\}\)
First form the union: \(B\cup C=\{0,3,4,5,6,9\}\), because every element appearing in either set is included once. Now intersect this result with \(A=\{1,3,5,7,9\}\). The common elements are 3, 5, and 9, so \(A\cap(B\cup C)=\{3,5,9\}\). Therefore option A is correct; option D is only the union, not the final intersection.
Frequently asked questions
What is the correct answer to this question?
\(\{3,5,9\}\)
Why is this the correct answer?
First form the union: \(B\cup C=\{0,3,4,5,6,9\}\), because every element appearing in either set is included once. Now intersect this result with \(A=\{1,3,5,7,9\}\). The common elements are 3, 5, and 9, so \(A\cap(B\cup C)=\{3,5,9\}\). Therefore option A is correct; option D is only the union, not the final intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
