I'm stuck on this question: Let A={1,2,3....,n}. What is the cardinality of the set: {(a,S) : a S, S P(A)}. I feel like its going to be related to 2^n, but i'm not sure. Could someone point me in the right direction?
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Let , then we are counting the number of ordered pairs in . There are subsets of that contain the number . So there are pairs in having as the first term. Therefore, how many pairs are there in
Why ? Surely it would be ?
No wait I see it now. So the answer should be ?
You have it.
Awesome, thanks for the help!
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