Did I list all the correct subsets of {a,b,c,d}?

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


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


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


{a,b,c,d}


Is there a mathematical way to calculate the number of sets to find? THANKS. I will give best answer

Did I list all the correct subsets of {a,b,c,d}?
As was mentioned, for a set with n elements, there are 2^n subsets, so this is a good way to check if you have all of them.





However, you have {b,d} twice (written once as {d,b}). You are forgetting the empty set, which is a subset of every set (and may have been what LuLu was referring to).





I think the easiest way to get all of them listed is, as you did, to get all the subsets of each size. However, I think it's easiest to work with the elements in order in each set. I think this would help make sure you don't repeat subsets.


{}


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


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


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


{a,b,c,d}





Notice also that the number of subsets with x elements is the binomial coefficient (or "choose" function), nCx. I don't think you'll need this fact, but it's handy to recognize that the number of subsets is symmetric. That is, one empty set and one full set, four sets of size 1 as well as of size 3, etc.
Reply:Yes, your list is correct, and yes, there is a way to calculate the number of subsets of a given set.





The set of all subsets of a given set P is called the "power set" of P. If P has n elements, the power set has 2^n elements (this works with your set: 2^4 = 16).





I first came across the proof of this during my first term at Cambridge :).
Reply:There is a way to discover how many results are possible, but with this you have to list the subsets, and yes that should be all.
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