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
Contradiction
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
Question being asked
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