1. Conditional Statements
Section May 15/16
Goal: To learn about and use conditional statments

2. Think About It…     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    

3. Vocabulary: 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)

4. Identify the Hypothesis and Conclusion of the following:
Examples:
Identify the Hypothesis and Conclusion of the following:
hypothesis (p)
conclusion (q)
If an animal is a robin, then the animal is a bird.
If an angle measures 130 degrees, it is obtuse.
Two points are collinear if they lie on the same line.
Note: Do not include the words “if” or “then.”
hypothesis (p)
conclusion (q)
hypothesis (p)
conclusion (q)

5. Examples:
Re-write the following conditional statements in if-then form. Then identify the Hypothesis (p) and Conclusion (q) of the following:
An object weighs one ton if it weighs 2000 pounds.
If an object weighs 2000 pounds, then it weighs one ton.
*A fish can swim.
If an animal is a fish, then it can swim.
hypothesis (p)
conclusion (q)
hypothesis (p)
conclusion (q)

6. Write a conditional statement to represent each Venn diagram.
Venn diagrams
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.

7. Venn diagrams
Is the conditional true or false? If it is false, find a counterexample.
If a number is divisible by three, then it is odd.
False is divisible by three and twelve is even
If a month has only 28 days, then it is February.
True
If two angles form a linear pair, then they are supplementary.
If an animal has spots, then it is a leopard
False- Dalmatians have spots and they are not leopards.

8. Negation “~”
To negate a statement, write the negative or opposite of that statement
Brenda likes pizza.
Monkeys eat bananas.
Ben does not play tennis.
Negation: Brenda does not like pizza.
Negation: Monkeys do not eat bananas.
Negation: Ben plays tennis.

9. Inverse …When you negate the hypothesis and the conclusion ~p  ~q
Write the inverse of the following statements.
If it rains, practice will be canceled.
If the battery is not charged, then the car will not start.
Inverse: If it does not rain, practice will not be cancelled.
Inverse: If the battery is charged, then the car will start.

10. converse …Switch the hypothesis and conclusion q  p
Write the converse of each statement.
If you see lightening, then you hear thunder
Converse: If you hear thunder, then you see lightening
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.

11. contrapositive
…Switch and negate the hypothesis and conclusion. ~q  ~p
If it is raining, I will go to the movies
If the sun is out, then the weather is good.
If a figure is a triangle, then it has three sides.
Contrapositive: If I do not go to the movies, then it is not raining.
Contrapositive: If the weather is not good, then the sun is not out.
Contrapositive: If a figure does not have three sides, then it is not a triangle.

12. Truth Value True False; A rectangle is a quad but is not a square.
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.
Converse: If a figure is a quadrilateral, then it is a square.
Inverse: If a figure is not a square, then it is not a quadrilateral.
Contrapositive: If a figure is not a quadrilateral, then it is not a square.
True
False; A rectangle is a quad but is not a square.
False; A rectangle is not a square but is a quad.
True
Notice that the Original and Contrapositive have the same truth value, and the Converse and Inverse have the same truth value.

13. Quick Notes
Conditional p  q Inverse ~p  ~q Converse q  p Contrapositive ~q  ~p