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Which binary relations are functions. Preferences, , Binary Relations, Utility Functions Suppose we continue to assume that a particular consumer s preference is described by a utility.

For instance, Functions between Small Sets Chris Boucher., a subset of A B, called abinary relation from A to B is a collection of ordered lations

Since all functions are binary relations, it is correct to use thefat] semicolon for function composition as well.

Binary relations establish a relationship between elements of two sets Definition: Let A , B be two sets A binary relation from A to B is a subset of AB. CS340 Discrete Structures Section 4 1 Page 3 Properties of Binary Relations: R is reflexive x R x for all x A Every element is related to itself.

Week 4 5: Binary Relations 1 Binary Relations functions To avoid confusion , we write S R as RS x z., for aesthetic reason

Binary Relations De nition: A binary relation between two sets X , Yor between the elements of X , Y) is a subset of X Y utility functions

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