# Subset Relations

#### fg9

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

#### pka

##### Elite Member
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.