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math challenge II-A combinatoratics 7.23

 
 
WuZeyin的头像
math challenge II-A combinatoratics 7.23
WuZeyin - 2021年10月1日 Friday 01:51
 

Why is n(B)=2^5? Isn't it all subsets of A?

 
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Re: math challenge II-A combinatoratics 7.23
LensmireJohn - 2021年10月1日 Friday 12:03
 

Yes $n(B) = 2^5 = 32$ is the number of subsets of $A$. How are you counting the number of subsets of $A$?

 
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WuZeyin的头像
Re: math challenge II-A combinatoratics 7.23
WuZeyin - 2021年10月1日 Friday 22:32
 
For every number in n(A) we either include it or not in n(B), which gives 2^5=32, but can we also not include anything? Shouldn’t we subtract this one possibility and give 31 before we make injections from A to B?
 
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Re: math challenge II-A combinatoratics 7.23
LensmireJohn - 2021年10月4日 Monday 12:47
 

Remember that the empty set $\emptyset = \{\}$, which is the set that contains nothing, is always a subset of any other set. Therefore, we do want to still include this outcome, giving us the $32$ subsets.

 
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