If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is \((A\cap B)^c\)?
Answer and explanation
Correct answer: \(\{1,2,4,5,6\}\)
The intersection contains elements common to both sets. Since 3 is the only common element, \(A\cap B=\{3\}\). The complement is formed by selecting elements of \(U\) that are not in this intersection. Thus \(U\setminus\{3\}=\{1,2,4,5,6\}\). Option A is correct. Option B is the intersection itself, option C still includes 3, and option D incorrectly claims that no elements remain.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,4,5,6\}\)
Why is this the correct answer?
The intersection contains elements common to both sets. Since 3 is the only common element, \(A\cap B=\{3\}\). The complement is formed by selecting elements of \(U\) that are not in this intersection. Thus \(U\setminus\{3\}=\{1,2,4,5,6\}\). Option A is correct. Option B is the intersection itself, option C still includes 3, and option D incorrectly claims that no elements remain.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
