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Exam 2

MAT 300 Mathematical Structures

Existential Instantiation Introducing a new variable x into the proof to stand for an object for which P(x) is true. This means that you can now assume that P(x) is true
Universal Instantiation You can plug in any value, say a, for x and use this given to conclude that P(a) is true.
m divides n (m|n) n is evenly divisible by m
Odd integers
Even integers
Uniqueness (E!)
Ordered pairs Pairs of values in which the order of the values makes a difference (a, b)
First coordinate The first value in an ordered pair, so a
Second coordinate The second value in an ordered pair, so b
Cartesian product (AxB) of two sets The set of all ordered airs in which the first coordinate is an element of A and the second is an element of B
Relations from A to B Suppose A and B are sets. Then a set R (is a subset of) AxB is called a relation from A to B
Domain of relations and functions p. 172
Range of relations and functions p. 172
Inverse of relations p. 172
Composition of relations and functions
Identity relation and function (iA) on a set A
Reflexive relations p. 184-185
Symmetric relations p. 184-185
Transitive relations p. 184-185
Antisymmetric relations p. 189
Partial orders A relation R on a set A that is reflexive, transitive, and antisymmetric
Total orders p. 190
Smallest element p. 189-
Largest element
Equivalence relations
Equivalence classes
A modulo R (A/R)
Congruence modulo
Functions f: A --> B
Codomain of a function
Created by: arianaflores