If \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5\}\), what is \((A\cup B)\cap C\)?
Answer and explanation
Correct answer: \(\{4\}\)
Evaluate the expression in the indicated order. First, \(A\cup B=\{1,2,3,4\}\), because all distinct elements from A and B are included. Next, intersect this result with \(C=\{4,5\}\). The only element common to both sets is 4, so \((A\cup B)\cap C=\{4\}\). Option B is wrong because 3 is not in C; option C is a union rather than the requested intersection, and option D ignores the common element 4.
Frequently asked questions
What is the correct answer to this question?
\(\{4\}\)
Why is this the correct answer?
Evaluate the expression in the indicated order. First, \(A\cup B=\{1,2,3,4\}\), because all distinct elements from A and B are included. Next, intersect this result with \(C=\{4,5\}\). The only element common to both sets is 4, so \((A\cup B)\cap C=\{4\}\). Option B is wrong because 3 is not in C; option C is a union rather than the requested intersection, and option D ignores the common element 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
