Conditional
Statements
SECTION 10.3
MAY 15/16
GOAL: TO LEARN ABOUT AND USE CONDITIONAL STATMENTS
IN
There is a law that states...
“If your windshield wipers are on,
then your headlights must be on.”
Or
 If wipers Then headlights

Assume the original statement is true….
Which, if any, MUST also be true?
 If headlights  Then wipers
 If no wipers  Then no headlights
 If no headlights Then no wipers



•
A Conditional is an if-then statement
•
The part that follows “if” is the Hypothesis( p )
•
The part that follows “then” is the Conclusion
(q)
Identify the Hypothesis and Conclusion
of the following:

conclusion (q)
hypothesis (p)
If an animal is a robin, then the animal is a bird.
Note: Do not include the words “if” or “then.”

hypothesis (p)
conclusion (q)
If an angle measures 130 degrees, it is obtuse.

hypothesis (p)
conclusion (q)
Two points are collinear if they lie on the same line.
Re-write the following conditional statements in
if-then form. Then identify the Hypothesis (p)
and Conclusion (q) of the following:
1.
An object weighs one ton if it weighs 2000 pounds.
If an object weighs 2000 pounds, then it weighs one ton.
conclusion (q)
hypothesis (p)
2.
*A fish can swim.
If an animal is a fish, then it can swim.
hypothesis (p)
conclusion (q)
Write a conditional statement to
represent each Venn diagram.
If a number is a
whole number then
it is an integer.
If a food is a wheat
product then it is a
grain.
Is the conditional true or false? If it
is false, find a counterexample.
If a number is divisible by three, then it is odd.
1.
•
False - 12 is divisible by three and twelve is even
If a month has only 28 days, then it is February.
2.
•
True
If two angles form a linear pair, then they are
supplementary.
3.
•
True
If an animal has spots, then it is a leopard
4.
•
False- Dalmatians have spots and they are not leopards.
To negate a statement, write the
negative or opposite of that statement
1.
Brenda likes pizza.
Negation: Brenda does not like pizza.
2.
Monkeys eat bananas.
Negation: Monkeys do not eat bananas.
3.
Ben does not play tennis.
Negation: Ben plays tennis.
…When you negate the hypothesis and the
conclusion
~p  ~q
Write the inverse of the following statements.
1.
If it rains, practice will be canceled.
Inverse: If it does not rain, practice will not
be cancelled.
2.
If the battery is not charged, then the car will not
start.
Inverse: If the battery is charged, then the
car will start.
…Switch the hypothesis and conclusion
qp

1.
Write the converse of each statement.
If you see lightening, then you hear thunder
Converse: If you hear thunder, then you see lightening
2.
If Allen gets a summer job, then he will bay a car.
Converse: If Allen buys a car, then he will get a summer
job.
…Switch and negate the hypothesis and
conclusion.
~q  ~p
1.
If it is raining, I will go to the movies
Contrapositive: If I do not go to the movies,
then it is not raining.
2.
If the sun is out, then the weather is good.
Contrapositive: If the weather is not good,
then the sun is not out.
3.
If a figure is a triangle, then it has three sides.
Contrapositive: If a figure does not have
three sides, then it is not a triangle.
Write the converse, inverse, and contrapositive and
state whether each is true or false. If false, provide a
counterexample.
Original Conditional: If a figure is a square, then it is a
quadrilateral.

True
Converse: If a figure is a quadrilateral, then it is a square.
False; A rectangle is a quad but is not a square.
Inverse: If a figure is not a square, then it is not a
quadrilateral.
False; A rectangle is not a square but is a quad.
Contrapositive: If a figure is not a quadrilateral, then it is
not a square. True
Notice that the Original and Contrapositive have the same truth value,
and the Converse and Inverse have the same truth value.
Conditional
Inverse
Converse
Contrapositive
pq
~p  ~q
qp
~q  ~p