If \(U=\{1,2,3,4\}\) and \(A=\{1,4\}\), which statement is correct?
Answer and explanation
Correct answer: \(2\in A^c\)
The complement of A consists of elements in U that are not in A. Since \(A=\{1,4\}\) and \(U=\{1,2,3,4\}\), we obtain \(A^c=\{2,3\}\). Therefore 2 belongs to \(A^c\), making option A true. Option B is false because 1 belongs to A, option C is false because 4 belongs to A, and option D is false because 3 is not in A. Membership must always be checked relative to U.
Frequently asked questions
What is the correct answer to this question?
\(2\in A^c\)
Why is this the correct answer?
The complement of A consists of elements in U that are not in A. Since \(A=\{1,4\}\) and \(U=\{1,2,3,4\}\), we obtain \(A^c=\{2,3\}\). Therefore 2 belongs to \(A^c\), making option A true. Option B is false because 1 belongs to A, option C is false because 4 belongs to A, and option D is false because 3 is not in A. Membership must always be checked relative to U.
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.
