Deductive Structure

Statements of Logic

The Structure

E u c lid e a n S truc tu re

D e fin e d T e rm s P o s tu la tes T h e ore m s

U n d efin e d T e rm sP o in tL ine

P la ne

Conditional Statement

HypothesisIf………

ConclusionThen………..

If a polygon has three sides , then it is a triangle.

Conditional Statements

If you study, then you will pass the test.Conditional statement

If you pass the test, then you study.Converse

If you do not study, then you will not pass the test.Inverse

If you do not pass the test, then you do not study.Contrapositive

Things to Remember

Definitions are always reversible

Theorems and postulates are sometimes reversible

Theorems must be proven

Postulates are accepted without proof

Conditional Notation

a b Conditional

b a Converse

b a Contrapositive

a b Inverse

Chain of Reasoning

If a b and b c, then a c

If you study hard, then you make good grades.If you make good grades, then you make money.If you make money, then you buy fast cars.If you buy fast cars, then you get speeding tickets.

If you study hard, then you get speeding tickets.

Theorem 3

If a conditional statement is true, then the contrapositive is also true

Example:

x y , z w , v y , v w