If \(A=\{p,q,r,s,t\}\), \(B=\{q,s,u\}\), and \(C=\{r,s,t,u\}\), what is \(A\setminus(B\cap C)\)?
Answer and explanation
Correct answer: \(\{p,q,r,t\}\)
Evaluate the parentheses first. The elements common to B and C are only s and u, so \(B\cap C=\{s,u\}\). Now remove from A every element that belongs to this intersection. The element s is in A and must be removed, but u is not in A and therefore has no effect. The remaining set is \(\{p,q,r,t\}\), which makes option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\{p,q,r,t\}\)
Why is this the correct answer?
Evaluate the parentheses first. The elements common to B and C are only s and u, so \(B\cap C=\{s,u\}\). Now remove from A every element that belongs to this intersection. The element s is in A and must be removed, but u is not in A and therefore has no effect. The remaining set is \(\{p,q,r,t\}\), which makes 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).
