If \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\), and \(C=\{3,5,11\}\), what is \(A\cap B\cap C\)?
Answer and explanation
Correct answer: \(\{3,5\}\)
An intersection contains only elements common to every set involved. The elements 3 and 5 occur in \(A\), in \(B\), and in \(C\). The elements 2 and 7 occur only in \(A\), while 1 and 9 occur only in \(B\), and 11 occurs only in \(C\). Hence the common intersection is \(A\cap B\cap C=\{3,5\}\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\{3,5\}\)
Why is this the correct answer?
An intersection contains only elements common to every set involved. The elements 3 and 5 occur in \(A\), in \(B\), and in \(C\). The elements 2 and 7 occur only in \(A\), while 1 and 9 occur only in \(B\), and 11 occurs only in \(C\). Hence the common intersection is \(A\cap B\cap C=\{3,5\}\), making option A 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).
