sept 25.notebook
September 25, 2015
Objectives:
Planner:
Sept 25, 2015
Pg 34 #6­16
sept 25.notebook
OMG
September 25, 2015
Biconditional Statement
Two statements connected by the words "if and only if"
sept 25.notebook
September 25, 2015
OMG
Converse
A version of a conditional statement formed by interchanging the hypothesis and conclusion of the statement.
ex:
If q then p.
sept 25.notebook
OMG
September 25, 2015
Contrapositive
A version of a conditional statement formed by interchanging and negating both the hypothesis and conclusion of the statement.
ex:
If not q then not p.
sept 25.notebook
OMG
September 25, 2015
Inverse
A version of a conditional statement formed by negating both the hypothesis and conclusion of the statement.
ex:
If not p then not q.
sept 25.notebook
OMG
September 25, 2015
Truth Values
The truth or falsity of a proposition
sept 25.notebook
September 25, 2015
sept 25.notebook
September 25, 2015
1. Given the conditional statement:
If a figure is a triangle, then it is a polygon.
Complete the table.
Form of the Write the Statement
Statement
Conditional Statement
Converse of the conditional statement
Inverse of the conditional statement
Contrapositive of the conditional statement
True or False
If the statement is false, give a counterexample.
sept 25.notebook
September 25, 2015
2. Write a true conditional statement whose inverse is false. sept 25.notebook
September 25, 2015
3. Write a true conditional statement that is logically equivalent to its converse. sept 25.notebook
September 25, 2015
4. Write the definition of perpendicular lines in biconditional form sept 25.notebook
September 25, 2015
sept 25.notebook
September 25, 2015
5. Consider the statement: Numbers that do not end in 2 are not even.
a. Rewrite the statement in if­then form and state whether it is true or false.
b. Write the converse and state whether it is true or false. If false, give a counterexample.
c. Write the inverse and state whether it is true or false.
d. Write the contrapositive and state whether it is true or false. If false, give a counterexample.
e. Can you write a biconditional statement for the original statement? Why or why not?
sept 25.notebook
September 25, 2015
Homework
Pg 34 #6­16