If \(|U|=9\), \(|A|=5\), and \(A\subseteq U\), what is the value of \(|\mathcal{P}(U-A)|\)?
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Answer and explanation
Correct answer: 16
Because \(A\subseteq U\), the difference \(U-A\) contains all elements of \(U\) that are not in \(A\). Its cardinality is \(|U-A|=|U|-|A|=9-5=4\). The power set of a four-element set contains \(2^4=16\) subsets. Therefore, \(|\mathcal{P}(U-A)|=16\), and option B is the correct answer.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Because \(A\subseteq U\), the difference \(U-A\) contains all elements of \(U\) that are not in \(A\). Its cardinality is \(|U-A|=|U|-|A|=9-5=4\). The power set of a four-element set contains \(2^4=16\) subsets. Therefore, \(|\mathcal{P}(U-A)|=16\), and option B is the correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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