I have to determine whether the $\subseteq$ relation is reflexive, symmetric, transitive and serial.
I'm slightly confused as to how to begin
I know that $A\subseteq B$ iff $\forall x (x\in A \rightarrow x\in B).$
And I have quantified definitions of reflexivity, symmetry, seriality, transitivity:
R is reflexive iff $\forall x Rxx$.
R is symmetrical iff $\forall x,y (Rxy \rightarrow Ryx)$.
R is transitive iff $\forall x,y,z (Rxy \land Ryz \rightarrow Rxz)$.
R is serial iff $\forall x \exists y Rxy.$
I understand these in the abstract. But I'm confused about how knowing the definitions of the relevant kinds of relations and the definition of $ \subseteq$ can help me determine whether $\subseteq$ is reflexive, symmetrical, transitive and/or serial.
Does anyone have any advice about how to proceed? (I've read through a similar question posted from 3 years ago but it does not help me understand how to go about doing this problem).