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empty set


triclino

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First of all, you very specifically asked "What is the definition of the empty set," triclino. Mr. Skeptic answered.

 

Secondly, that definition does help. The set {D} is not a subset of the set {A,B,C}. Nor are {A, E} and {A,B,C,F}. Why is that?

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O.k this a trivial proof and i am waiting for another trivial proof :

 

Suppose x does not belong to the set ,A .But x does not belong to the empty set.

 

Hence if x does not belong to A ,then x does not belong to the empty set .

 

Thus : [math]\emptyset\subseteq A[/math]

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O.k this a trivial proof and i am waiting for another trivial proof :

 

Suppose x does not belong to the set ,A .But x does not belong to the empty set.

 

Hence if x does not belong to A ,then x does not belong to the empty set .

 

Thus : [math]\emptyset\subseteq A[/math]

 

That is almost correct, but you are missing one line. The definition of subset is:

 

A is a subset of B means that for all x in A, x is in B.

 

You haven't come up with that precise statement for the empty set and A, so you still need one more line. You are quite close, though.

=Uncool-

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