1. Examples: If a figure in convex, then it is an octagon.
Conditionals & Converses
Name:_________ Date:__
Complete the following Notes:
Conditional Statement ____________________________________________________
_____________________________________________________________
Antecedent _____________________________________________________________
Conclusion _____________________________________________________________
Proving Conditionals True _________________________________________________
Proving Conditional False _________________________________________________
Instance of a Conditional __________________________________________________
Counterexample of a Conditional ____________________________________________
Examples: If a figure in convex, then it is an octagon.
If a figure is an pentagon then it is a polygon.

2. Examples:
If a figure is discrete, then it is a line.
If a line is dense, then it is vertical.
If the equation of line is y = x, then it is oblique.
Converse: _________________________________________________
_________________________________________________
Write the converse for each of the four “if-then” statements above.
__________________________________________________________

3. A conditional is only true if it is ALWAYS true.
Conditionals & Converses
Name:_________ Date:__
Complete the following Notes:
Conditional Statement ____________________________________________________
_____________________________________________________________
Antecedent _____________________________________________________________
Conclusion _____________________________________________________________
Proving Conditionals True _________________________________________________
Proving Conditional False _________________________________________________
Instance of a Conditional __________________________________________________
Counterexample of a Conditional ____________________________________________
Called an “if-then” statement, either contains
the words “if-then” or can be rewritten to contain them.
Also called the hypothesis, is the phrase following
the word if (or could follow the word if when
rewriting the sentence).
Also called the consequent, is the phrase
following the word then (or could follow the word
then when rewriting the sentence).
A conditional is only true
if it is ALWAYS true.
A conditional is false if it is
SOMETIMES or NEVER true.
Is an example that is true for BOTH
the antecedent/hypothesis and the
conclusion/consequent.
Is an example that is true for
the antecedent/hypothesis and false
for the conclusion/consequent.
Examples: If a figure in convex, then it is an octagon.
If a figure is an pentagon then it is a polygon.

4. ? Think to yourself, “can a figure be convex and NOT be an octagon?”
Examples: If a figure in convex, then it is an octagon.
If a figure is a pentagon then it is a polygon.
Think to yourself, “can a figure be convex and
NOT be an octagon?”
instance
counter-
example
So the statement, If a figure in convex, then
it is an octagon is FALSE.
Think to yourself, “can a pentagon
NOT be an polygon?”
instance ? NO
counterexample
So the statement, If a figure is an pentagon
then it is a polygon, is TRUE.

5. So this statement is FALSE
Examples:
If a figure is discrete, then it is a line.
If a line is dense, then it is vertical.
If the equation of line is y = x, then it is oblique.
Converse: _________________________________________________
_________________________________________________
Write the converse for each of the three “if-then” statements above.
__________________________________________________________
So this statement is FALSE
instance
counterexample
By the way, these were examples that were neither instances or counterexamples
So this statement is FALSE
By the way, these were examples that were neither instances or counterexamples
counterexample
instance
So this is TRUE
y=3-x, neither
y=2, neither
y=x, instance
x=2, neither

6. The write a converse, switch the phrases (but not the words if-then).
_________________________________________________
Write the converse for each of the three “if-then” statements above.
__________________________________________________________
If , then
a figure is discrete
it is a line
So the converse is “If it is a line, then it is dense”