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I am a little confused on the WebWork problem which states
"A computer is printing out subsets of a 4 element set (possibly including
the empty set).
(a) At least how many sets must be printed to be sure of having at least 2
identical subsets on the list?
(b) At least how many identical subsets are printed if there are 49 subsets
on the list? "
what are you considering elements in the set? I am having a hard time
visualizing what the problem is asking for. If you could clarify this for
me I would be very grateful.
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This problem is designed to confuse, especially for those who never had a firm grasp on the notion of the power set P(S), which has elements that are subsets of S. In your case, the subsets of a four element set like {a,b,c,d} are the elements of the power set P({a,b,c,d}). A critical first step for you is to understand how many elements does this power set have? Now how many of these elements chosen at random (with repetition allowed) do you need to write down, before you are *guaranteed* that you have written down at least one element (i.e. some subset of {a,b,c,d}) twice? If you write down 49 subsets (49 elements of P({a,b,c,d}), what is the smallest number of elements that must be duplicates? (For instance if you got to pick the elements, you could choose all 49 the same and would have 49 duplicates--but this question is asking about a lower bound, not an upper bound)
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