6
Relations
Let R be a relation on a set A, i.e., a subset of AxA.
Notation: xRy i (x, y ) R AxA.
Recall: A relation need not be a function.
Example: The relation R1 = cfw_(x, y ) RxR | x2 + y 2 = 1 is
not a function.
Some denitions
1. R is reexive if xRx
4
Functions
Before studying functions we will rst quickly dene a more
general idea, namely the notion of a relation. A function
turns out to be a special type of relation.
Denition: Let S and T be sets. A binary relation on SxT
is any subset of SxT . A bi
Lecture Notes for Discrete Math
Douglas Bauer
1
Symbolic Logic
Denition: A proposition is a sentence that is true or false
but not both.
10 is a prime number
4x2=8
George Washington was mayor of N.Y.C.
This class has 35 students
Note: x > 4 is not a pr