| Summary: |
In this final unit of the current block we introduce the mathematical concept of relations between sets. We look at how relations differ from functions while noting that a function is actually a special types of relation. Different ways in which relations can be represented are discussed and include ordered pairs, arrow diagrams, matrices and directed graphs. Inverse and composite relations are briefly addressed before we investigate different types of relations (reflexive, symmetric and transitive) and methods for their classification. The important concepts of equivalence relations and equivalence classes are then described along with their properties. In closing the unit we look at the connection between equivalence relations and partitions of sets. The text is supported throughout with relevant examples and where appropriate references for further reading are provided. |
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