If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\), and \(C=A-B\), what is \(C\)?
Answer and explanation
Correct answer: \(\{1,3,5\}\)
To calculate \(A-B\), inspect each element of A and retain it only if it is not in B. Elements 2 and 4 occur in B, so they are removed. Element 6 is in B but not in A, so it cannot appear in \(A-B\). The remaining elements are 1, 3, and 5; hence \(C=A-B=\{1,3,5\}\). Therefore option A is correct, while the other options represent retained, removed, or unchanged elements incorrectly.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5\}\)
Why is this the correct answer?
To calculate \(A-B\), inspect each element of A and retain it only if it is not in B. Elements 2 and 4 occur in B, so they are removed. Element 6 is in B but not in A, so it cannot appear in \(A-B\). The remaining elements are 1, 3, and 5; hence \(C=A-B=\{1,3,5\}\). Therefore option A is correct, while the other options represent retained, removed, or unchanged elements incorrectly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
