Deductive Structure
Lesson 1.7
Deductive Structure:
Conclusions are
justified by means
of previously
assumed or
provided
statements.
Four Elements:
1.Undefined terms
2.Assumptions known as
postulates
3.Definitions
4.Theorems and other
conclusions
Postulate: an unproven
assumption
Definition: states the
meaning of a term, they
are ALWAYS reversible!
Example stated:
1 If a point is the midpoint of a
segment, then the point
divides the segment into 2
congruent segments.
2 If a point divides a segment
into 2 congruent segments,
then the point is midpoint of
the segment.
Conditional Statement:
P hypothesis: “If ” part of
the statement.
Q conclusion: “Then” part
of the statement.
LOGIC:
p
q (read) “If p, then q.”
“p implies q.”
Converse:
Of p implies q is q implies p
p
q
q
p
Theorem: math statement you
can prove
Come with number
Can‟t use T1 to prove T1
Theorems and postulates are
not always reversible!
If 2 <“s are right <„s, then they
are congruent. True
Converse:
If 2 <„s are congruent, then
they are right <„s.
False
T or F?
Conditional
statement and converse.
If an animal is a dog, then it has
four legs.
If it has four legs, then the
animal is a dog.
False!
If a student receives a B on the
test, then his/her grade is
between 80 and 90.
State the converse and tell if
it is T or F.
If the students grade is between
80 and 90, then the student
receives a B on the test. True