3.3:
A
conditional
statement is a compound statement that uses the connective
if…
then
. Written with an arrow p > q. p is the
antecedent
and q is the
consequent
.
For
conditional
: TT=T TF=F FT=T FF=T.
Negation
of p > q is p ^ ~q.
Conditional
as “or” statement
: ~p v q.
3.4
: Flipping the conditional is the
converse
q > p
.
Negating both antecedent and consequent is the
inverse
~p > ~q. The
contrapositive
is both interchanged and negated ~q > ~p.
Equivalences
: A
conditional statement and its contrapositive are equivalent, and the converse and the
inverse are equivalent.
Biconditionals
:
p
if and only if
q , symbolized as p <> q.
For
biconditiona
l: TT=T TF=F FT=F FF=T.
4.1
: A
mathematical syst
em is made up
of three components: 1. A set of elements 2. One or more operations for combining
the elements 3. One or more relations for comparing the elements. Various ways of
symbolizing and working with counting numbers are called
numeration systems
.
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 Spring '08
 Heatwole
 Math, Set Theory, Natural number, Numeral system

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