Set notation

use of set language and the following notation:

• Union of $A$ and $B$: $A \cup B$
• Intersection of $A$ and $B$: $A \cap B$
• Number of elements in set $A$: $n(A)$
• '$\ldots$ is an element of $\ldots$': $\in$
• '$\ldots$ is not an element of $\ldots$': $\notin$
• Complement of set $A$: $A'$
• The empty set: $\varnothing$
• Universal set: $\xi$
• $A$ is a subset of $B$: $A \subseteq B$
• $A$ is not a subset of $B$: $A \nsubseteq B$
• $A$ is a (proper) subset of $B$: $A \subset B$
• $A$ is not a (proper) subset of $B$: $A \not\subset B$