Subset Relations

[fg9]

When "A" is a subset of "B", is the relation "antisymmetric", "transitive" or "reflexive"?

 

[pka]

When "A" is a subset of "B", is the relation "antisymmetric", "transitive" or "reflexive"?

In set theory we use \(A\mathcal{R} B\) to read \(A\) is related to \(B\) or in this case \(A\subseteq B\)
1) If \(A\mathcal{R} B~\&~B\mathcal{R} A\) does that mean \(A= B~?\) If so the it is antisymmetric.
2) If \(A\mathcal{R} B~\&~B\mathcal{R} C\) does that mean that \(A\mathcal{R} C~?\) If so the it is transitive.
3) If for each set \(A\mathcal{R} A\) then it is reflexive.