(New page: Category:Set Theory Category:Math == Theorem == The empty set Ø is a subset of every set including itself and the universal set ''S''<br/> i.e. Ø ⊆ A ∀A ⊆ ''S''. ----...) |
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==Proof== | ==Proof== | ||
| − | By definition of the subset, Ø ⊆ A is true because all of the elements in Ø (of which there are none) are in A. Thus Ø ⊆ A is vacuously true. | + | By definition of the subset, Ø ⊆ A is true because all of the elements in Ø (of which there are none) are in A. Thus Ø ⊆ A is vacuously true. <br/> |
<math>\blacksquare</math> | <math>\blacksquare</math> | ||
Latest revision as of 05:20, 6 October 2013
Theorem
The empty set Ø is a subset of every set including itself and the universal set S
i.e. Ø ⊆ A ∀A ⊆ S.
Proof
By definition of the subset, Ø ⊆ A is true because all of the elements in Ø (of which there are none) are in A. Thus Ø ⊆ A is vacuously true.
$ \blacksquare $
