If \(U=\{5,10,15,20\}\) and \(A=U\), what is \(A^c\)?
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Answer and explanation
Correct answer: \(\varnothing\)
The complement is defined as A^c=U−A, the set of elements in U that are not in A. Here A and U contain exactly the same four elements: 5, 10, 15, and 20. Since every element of U has already been included in A, no element remains outside A. Consequently, A^c is the empty set, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The complement is defined as A^c=U−A, the set of elements in U that are not in A. Here A and U contain exactly the same four elements: 5, 10, 15, and 20. Since every element of U has already been included in A, no element remains outside A. Consequently, A^c is the empty set, so option A is correct.
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.
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