If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,e,f\}\), what is \(A\cap B\)?
Answer and explanation
Correct answer: \(\{c,e\}\)
The intersection \(A\cap B\) contains only elements common to both sets. Comparing \(A=\{a,c,e\}\) with \(B=\{b,c,e,f\}\), the common elements are c and e. Therefore, \(A\cap B=\{c,e\}\). The universal set is not automatically the answer; a letter belongs to the intersection only when it is listed in both A and B.
Frequently asked questions
What is the correct answer to this question?
\(\{c,e\}\)
Why is this the correct answer?
The intersection \(A\cap B\) contains only elements common to both sets. Comparing \(A=\{a,c,e\}\) with \(B=\{b,c,e,f\}\), the common elements are c and e. Therefore, \(A\cap B=\{c,e\}\). The universal set is not automatically the answer; a letter belongs to the intersection only when it is listed in both A and B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
