**Proper subset definition**

A proper subset of a
set AA is a

__subset__of AA that is not equal to AA. In other words, if BB is a proper subset of AA, then all elements of BB are in AA but AA contains at least one element that is not in BB.
For
example, if A={1,3,5}A={1,3,5} then B={1,5}B={1,5} is a
proper subset of AA. The set C={1,3,5}C={1,3,5} is a subset
of AA, but it is not a proper subset of AA since C=AC=A.
The set D={1,4}D={1,4} is not even a subset of AA, since 4 is
not an element of AA.

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