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.