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#1 2006-01-08 02:06:44
- Saiyan
- Guest
Sets (Subsets and Proper Subsets)
Hello everyone,
I really don't understand this.
S = {Fred, Sue, Ashraf}
{Fred, Ashraf} Subset of S
{Fred, Ashraf} ProperSubset of S
how can {Fred,Ashraf} be a proper Subset and ALSO be a subset ???
#2 2006-01-08 05:36:38
- Ricky
- Moderator
Offline
Re: Sets (Subsets and Proper Subsets)
Set A is a subset of set B if for every element in A, that element exists in B.
Set A is a proper subset of set B if A is a subset of B, but B is not a subset of A.
So {Fred, Ashraf} is a subset of S because both Fred and Ashraf are in S.
But S is not a subset of {Fred, Ashraf} because Sue is not in {Fred, Ashraf}
Now take it one step further:
Prove that if A is a proper subset of B, then A is a subset of B.
Proof: For A to be a proper subset of B, A must be a subset of B.
Therefore A is a subset of B. QED.
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