subset

• A is a subset of B, and B is a superset of A ⇐> every element of A is also element of B
• (A is subset of set B: $A\subseteq B$) = (B is superset of set A: $B\supseteq A$)
• Theorem 4: For every set S, (i) $\varnothing \subseteq S$, (ii) $S\subseteq S$
• Remark 1: A is proper subset of B if (i) A is a subset of B (ii) $A\ne B$
• Remark 2: $A\subseteq B$ and $B\subseteq C$ ⇒ $A=B$