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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.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."