If \(U=\{x:x\text{ is an alphabet letter}\}\) and \(A=\{x:x\text{ is a vowel}\}\), what does \(A^c\) represent?
Answer and explanation
Correct answer: \(\{x:x\text{ is a consonant}\}\), the set of consonants
A complement is always defined with respect to its universal set. Here U contains all alphabet letters, while A contains the vowels. Therefore \(A^c=U\setminus A\) contains every alphabet letter that is not a vowel. These letters are the consonants, so option A is correct. The answer depends on the given universe: it is not the empty set or all of U, and it is not A itself because A contains vowels.
Frequently asked questions
What is the correct answer to this question?
\(\{x:x\text{ is a consonant}\}\), the set of consonants
Why is this the correct answer?
A complement is always defined with respect to its universal set. Here U contains all alphabet letters, while A contains the vowels. Therefore \(A^c=U\setminus A\) contains every alphabet letter that is not a vowel. These letters are the consonants, so option A is correct. The answer depends on the given universe: it is not the empty set or all of U, and it is not A itself because A contains vowels.
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.
