If \(U=\{apple, banana, grapes, mango\}\) and \(A=\{apple, mango\}\), what is the complement \(A'\) of \(A\) with respect to \(U\)?
Answer and explanation
Correct answer: \(\{banana, grapes\}\)
The complement of \(A\) relative to \(U\) is \(A'=U\setminus A\), meaning all elements that are in the universal set but not in \(A\). Removing apple and mango from \(U=\{apple, banana, grapes, mango\}\) leaves banana and grapes. Therefore \(A'=\{banana, grapes\}\), represented by option B. Option A is the original set, option C incorrectly retains mango, and option D is not empty.
Frequently asked questions
What is the correct answer to this question?
\(\{banana, grapes\}\)
Why is this the correct answer?
The complement of \(A\) relative to \(U\) is \(A'=U\setminus A\), meaning all elements that are in the universal set but not in \(A\). Removing apple and mango from \(U=\{apple, banana, grapes, mango\}\) leaves banana and grapes. Therefore \(A'=\{banana, grapes\}\), represented by option B. Option A is the original set, option C incorrectly retains mango, and option D is not empty.
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.
