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Exam 2
MAT 300 Mathematical Structures
Term | Definition |
---|---|
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 | |
Partitions | |
A modulo R (A/R) | |
Congruence modulo | |
Functions f: A --> B | |
Codomain of a function |