If \(A=\{1,2,3,4\},\; B=\{2,4,6\},\) and \(C=\{1,2,6\},\) what is \((A\cap B)\cup C\)?
Answer and explanation
Correct answer: \(\{1,2,4,6\}\)
First evaluate the intersection because the expression contains parentheses: \(A\cap B\) consists of elements common to both A and B, so \(A\cap B=\{2,4\}\). Next take the union with C, which includes every distinct element in either set: \(\{2,4\}\cup\{1,2,6\}=\{1,2,4,6\}\). Thus option A is correct. Option B stops after the intersection, option C ignores the intersection, and option D incorrectly includes 3, which is not in the intermediate result or C.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,4,6\}\)
Why is this the correct answer?
First evaluate the intersection because the expression contains parentheses: \(A\cap B\) consists of elements common to both A and B, so \(A\cap B=\{2,4\}\). Next take the union with C, which includes every distinct element in either set: \(\{2,4\}\cup\{1,2,6\}=\{1,2,4,6\}\). Thus option A is correct. Option B stops after the intersection, option C ignores the intersection, and option D incorrectly includes 3, which is not in the intermediate result or C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
