If \(U=\{7,8,9\}\) and \(A=\varnothing\), what is \(A^c\)?
Answer and explanation
Correct answer: \(U\)
The complement A^c contains all elements of U that are not in A. Since A is the empty set, it contains no elements to remove from U. Therefore every element of U remains in the complement, giving A^c=U={7,8,9}. This is the standard identity ∅^c=U. Options C and D contain only part of U, while option B incorrectly repeats the empty set.
Frequently asked questions
What is the correct answer to this question?
\(U\)
Why is this the correct answer?
The complement A^c contains all elements of U that are not in A. Since A is the empty set, it contains no elements to remove from U. Therefore every element of U remains in the complement, giving A^c=U={7,8,9}. This is the standard identity ∅^c=U. Options C and D contain only part of U, while option B incorrectly repeats the empty set.
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.
