Math Is Fun Forum

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 ???

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

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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"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..."