Conditional Statements
Section 2-2
Objective
• Students will be able to recognize
conditional statements and their parts to
write converses, inverses, and
contrapositives of conditionals.
Conditional Statements
If-then statements are called
conditional statements.
The portion of the sentence following if
is called the hypothesis. The part
following then is called the
conclusion.
p
q (If p, then q)
p
q
If it is an apple, then it is a fruit.
Hypothesis – It is an apple.
Conclusion – It is a fruit.
A conditional can have a truth
value of true or false.
Using a Venn Diagram to illustrate
a conditional
q
p
Converse q
p
The converse statement is formed
by switching the hypothesis and
conclusion.
If it is an apple, then it is a fruit.
Converse: If it is a fruit, then it is an
apple.
The converse may be true or false.
Underline the hypothesis and circle the
conclusion for each conditional statement, then
write the converse.
1. If you are an American citizen, then you
have the right to vote.
2. If a figure is a rectangle, then it has four
sides.
Write each sentence as a conditional statement.
1. A point in the first quadrant has two positive
coordinates.
If a point is in the first quadrant, then it has two
positive coordinates.
1. Thanksgiving in the U.S. falls on the fourth
Thursday of November.
If it is Thanksgiving in the U.S., then it is the
fourth Thursday of November.
Using a Venn Diagram to illustrate
a conditional
Illinois
Residents
Chicago
Residents
If you live in Chicago, then you live in
Illinois.
Get a Partner!
1. Each of you need to write 5 conditional
statements and draw 5 venn diagrams
2. Trade papers
3. Write the converse of each conditional statement
your partner wrote.
Biconditionals
• Remember: If your original conditional statement
is true and your converse is true, then you can
write a biconditional. p↔q read as “p if and only
if q” we can shorten it to “p iff q”.
• When either or both of your condition and the
converse is false, then you must write a counter
example. Why is it false?
• See page 78 for sample problems! 
The new stuff for today:
negation – the denial of a
statement (the opposite)
Ex. “An angle is obtuse.”
Negation – “An angle is not
obtuse.”
Inverse ~p
~q
An inverse statement can be formed
by negating both the hypothesis and
conclusion.
If it is an apple, then it is a fruit.
Inverse: If it is not an apple, then it is
not a fruit.
The inverse may be true or false.
Contrapositive ~q
~p
A contrapositive is formed by negating the
hypothesis and conclusion of the
converse.
If it is an apple, then it is a fruit.
Contrapositive: If it is not a fruit, then it is
not an apple.
The contrapositive of a true conditional is
true and of a false conditional is false.
Truth Table
p→q
q→p
T T
T
T
T
T
T
T
T F
F
T
T
F
F
T
F T
T
F
F
T
F
T
F
T
T
T
T
F
F
q
F
Contrapositive
“or”
Converse
p
Inverse
“And”
Conditional
~p → ~q ~q → ~p pnq pUq
Which columns are congruent? These are called equivalent
statements, because they have the same truth values!
Assignment:
• P. 93 (15-45) x’s of 3
• Ask me about the OPTIONAL project!