Question 169812: Of all theses sets which ones are proper 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} I know that the empty set is a proper subset and I think that the next 4 after that are as well but I am not sure about the other ones, any help would be appreciated.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! Proper subsets of what? You did not specify the original set, so the question as stated cannot be answered. However...
A proper subset must be strictly contained, therefore must exclude at least one element of the original set.
The empty set is a proper subset of any non-empty set.
So:
If the original set was the set of all lower case letters of the English alphabet, then all of the listed subsets would be proper.
If the original set was the set {a, b, c, d} then all of the listed subsets with the exeception of the very last one would be proper subsets.
If the original set was the set {a, b, d}, then any of the listed sets containing the element 'c' or any of the listed sets with 3 or more elements would NOT be proper subsets, while all of the rest would be.
Hope that helps. And, in the future, give us the WHOLE problem to work with. Thanks.
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