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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 ???
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..."
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