Definition 5.5 (Subsets and Supersets)

Let A, B be sets

1. A is a $\text{subset}$ of B (short: $A\subseteq B$), if every element of A is also an element of B
2. A is a $\text{proper subset}$ of B (short: $A⊊B$), if $A\subseteq B$ and $A\ne B$
3. A is a $\text{superset}$ of B (short: $A\supseteq B$), if $B\subseteq A$
4. A is a $\text{proper superset}$ of B (short: $A⊋B$), if $A\supseteq B$ and $A\ne B$

Remark

Alternative notation for $⊊:$ $\subset$