#### Discrete Mathematics

Conjunction

P and Q Symbol - "/\

Disjunction

NOT"Symbol - " \/

Negation

NOT"Symbol - "~

Exclusive OR

True if one of P or Q is True

DeMorgan Laws

0

Conditional Statement

A logical statement that has two parts, a hypothesis and a conclusion

Bi Conditional

<=>"p if and only if q"p is a hypothesis q is a conclusion

Tautology

all True statement

all false statements

Compound Statement

one or more logical connectives,needs to decide whether its T or F

Declare Sentence

Something is being declared

Interrogative Sentence

Imperative Sentence

Command is given

Exclamatory Sentence

Emotional expression

Inclusive OR

P or Q (same as disjunction)

Implications

P => Q Hypothesis - pConclusion - QFalse only when Hypothesis P is True and the Conclusion Q is False"If , then

Cardinality

|X| = the number of elements in X

intersection

a set containing all of the elements found in both of two set

union

a set containing all of the elements found in either of two sets

complement

the set containing all elements not in another set

ordered pair

a set of two elements (a, b) which is distinct from (b, a)

Cartesian product

a form of set multiplication, resulting in a set of ordered pairs

domain

domainX in f : X -> Y

co domain

Y in f: X -> Y

Range

the set of y in Y such that f(x) = y for some x in X

inverse

the function f^-1: Y -> X in relation to the one-to-one, onto function f: X -> Y

relation

a set of ordered pairs connecting two sets

reflexive

describes a relation on a set X in which (x,x) in R for every x in X

symmetric

describes a relation on a set X in which, for every x,y in X, if (x,y) is in R, (y,x) is in R

transitive

describes a relation on a set X in which, for every x,y,z in X, if (x,y) in R and (y,z) in R, (x,z) in R

equivalence relations

relations which are reflexive, symmetric, and transitive

permutation

an ordering of objects

combination

a selection of objects with no regards to order

n!

number of ordered selections of n objects with no repetitions6! = 6x5x4x3x2x1