## Union of Sets

 4.2 Union of Sets
Determine and describe the union of sets using various representation

• The union of sets $$P$$ and $$Q$$ is written using the symbol $$\cup$$.
• $$P \cup Q$$ represents all the elements in set $$P$$ or set $$Q$$ or in both sets $$P$$ and $$Q$$.
• Union of three sets, $$A$$, $$B$$ and $$C$$, represented as $$A∪ B ∪ C$$, is a set whose elements consist of all the elements in a set $$A$$, a set $$B$$ or a set $$C$$ or all three sets.

 Example Three private travel agencies, $$A, B$$ and $$C$$ are chosen to organise the tourism exhibition 2021 in Sarawak.  Several division in Sarawak are chosen to hold the exhibition as follows $$\xi= \text{Kapit, Miri, Bintulu, Sibu, Limbang, Mukah, Kuching, Betong}$$ $$A=\text{Miri, Sibu, Kuching, Betong}$$ $$B=\text{Miri, Sibu, Kapit, Limbang}$$ $$C=\text{Miri, Betong, Kapit, Mukah}$$ List all the elements of the following sets $$( A \cup B) '$$ Solution $$( A \cup B) = \text{Kapit,Miri, Sibu, Limbang, Kuching, Betong}$$ $$( A \cup B) ' = \text{Mukah, Bintulu}$$