If \(x\in A^c\), which statement is definitely true?
Answer and explanation
Correct answer: \(x\in U\) and \(x\notin A\)
Membership in A^c means that x belongs to the universal set U but does not belong to A. This follows directly from the definition A^c=U−A. Therefore both statements in option A must be true simultaneously. Option B places x in A, which contradicts complement membership; option C contradicts x being in U; and option D violates the disjointness of A and A^c.
Frequently asked questions
What is the correct answer to this question?
\(x\in U\) and \(x\notin A\)
Why is this the correct answer?
Membership in A^c means that x belongs to the universal set U but does not belong to A. This follows directly from the definition A^c=U−A. Therefore both statements in option A must be true simultaneously. Option B places x in A, which contradicts complement membership; option C contradicts x being in U; and option D violates the disjointness of A and A^c.
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.
