Areteem: math challenge II-A combinatoratics 7.23

Online Course Discussion Forum

math challenge II-A combinatoratics 7.23

math challenge II-A combinatorics 7.21
7.7 Math Challenge IIA Number Theory

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

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

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?

Show parent

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.

Show parent

math challenge II-A combinatorics 7.21
7.7 Math Challenge IIA Number Theory