If \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\), and \(C=\{3,4,7\}\), what is \(A\cap(B\cup C)\)?
Answer and explanation
Correct answer: \(\{2,3,4\}\)
First evaluate the expression inside parentheses: \(B\cup C=\{2,3,4,6,7\}\). Next find the elements common to this set and \(A=\{1,2,3,4,5\}\). The common elements are 2, 3, and 4, so \(A\cap(B\cup C)=\{2,3,4\}\). Option D is only the union and includes 6 and 7, which are not in \(A\); option B contains elements excluded from the union.
Frequently asked questions
What is the correct answer to this question?
\(\{2,3,4\}\)
Why is this the correct answer?
First evaluate the expression inside parentheses: \(B\cup C=\{2,3,4,6,7\}\). Next find the elements common to this set and \(A=\{1,2,3,4,5\}\). The common elements are 2, 3, and 4, so \(A\cap(B\cup C)=\{2,3,4\}\). Option D is only the union and includes 6 and 7, which are not in \(A\); option B contains elements excluded from the union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
