If \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\), and \(C=\{1,5,25\}\), what is \((A\cap B)\cup(B\cap C)\cup(C\cap A)\)?
Answer and explanation
Correct answer: \(\{1\}\)
Compare the sets pair by pair. The elements common to A and B are only 1, so \(A\cap B=\{1\}\). The elements common to B and C are also only 1, so \(B\cap C=\{1\}\). Finally, the elements common to C and A are only 1, so \(C\cap A=\{1\}\). Taking the union of these three pairwise intersections still gives \(\{1\}\), because repeating an element does not create a new element in a set. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1\}\)
Why is this the correct answer?
Compare the sets pair by pair. The elements common to A and B are only 1, so \(A\cap B=\{1\}\). The elements common to B and C are also only 1, so \(B\cap C=\{1\}\). Finally, the elements common to C and A are only 1, so \(C\cap A=\{1\}\). Taking the union of these three pairwise intersections still gives \(\{1\}\), because repeating an element does not create a new element in a set. 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).
