If the universal set is \(U=\{a,b,c,d,e\}\) and \(B=\{a,e\}\), how many elements does \(B^c\) contain?
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Answer and explanation
Correct answer: 3
The complement is found by removing the elements of \(B\) from the universal set: \(B^c=U\setminus B=\{b,c,d\}\). This set has three elements, so option B is correct. The answer is not 5, because 5 is the cardinality of the entire universal set, not the number of elements outside \(B\).
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The complement is found by removing the elements of \(B\) from the universal set: \(B^c=U\setminus B=\{b,c,d\}\). This set has three elements, so option B is correct. The answer is not 5, because 5 is the cardinality of the entire universal set, not the number of elements outside \(B\).
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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