Union of Two Sets

UNION
\({A \cup B}\), \({A}\) or \({B}\) , elements which are in \({A}\) or in \({B}\) .

Consider the set \({A = \{4, 5, 6, 7, 8\}}\) and \({B = \{7, 8, 9\}}\), all the elements in \({A}\) or in \({B}\) together is \({\{4, 5, 6, 7, 8, 9\}}\).

\({\therefore A \cup B = \{4, 5, 6, 7, 8, 9\}}\)

Note:
If \({A}\) is a subset of \({B}\), i.e., \({A \subseteq B}\), then \({A \cup B = B}\).

De Morgan's Law:
\({(A \cup B)' = A' \cap B'}\)
\({(A \cap B)' = A' \cup B'}\)
Principle of Inclusion and Exclusion:
\({n(A \cup B) = n(A) + n(B) - n(A \cap B)}\)