Question 202305
I'll do the first one to get you started




Recall, the number of subsets for set A is {{{2^(n(A))}}} where {{{n(A)}}} is the number of elements in set A.



So basically, to find the number of subsets for set A, simply count the number of elements in set A and then raise that number as a power with 2 as the base.





To save ourselves from writing out <i>every</i> subset (and potentially making mistakes), we can simply use the given formula to find the number of possible subsets.


Since n(A) = 5, this means that the possible number of subsets for A is



{{{2^5=32}}}



So there are 32 possible subsets for A



Note: even though set A has 5 elements, this generates 32 possible subsets. So we have saved ourselves from a lot of busy work.



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Here's a much simpler example:



Let A = {a, b, c}



The subsets of A are:


{a, b, c},
{a, b}, {a, c}, {b, c},
{a}, {b}, {c},
{ }


So there are 8 subsets



Take note that {{{2^3=8}}}. In other words, there are 3 elements and 2 cubed gets us 8 possible subsets.