ex:
A={j,o,y}
subsets: {j}, {o}, {y}
{j,o}, {j,y}, {o,y}
{j,o,y}, {}
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A is a subset of a set B if every element of A is also an element of B.
NO- by definition a set is not a proper subset of itself . ( It is a subset, but not a proper one. )
no. A subset would have to allow for values in its parent which are not in its self.
The set of Rational Numbers is a [proper] subset of Real Numbers.
The definition of subset is ; Set A is a subset of set B if every member of A is a member of B. The null set is a subset of every set because every member of the null set is a member of every set. This is true because there are no members of the null set, so anything you say about them is vacuously true.