1. Lesson 2.2 Analyze Conditional Statements
Objective: The learner will write definitions as conditional statements.

2. Determine if each statement is true or false.
Warm Up
Determine if each statement is true or false.
1. The measure of an obtuse angle is less than 90°.
2. All perfect-square numbers are positive.
3. Every prime number is odd.
4. Any three points are coplanar. F T F T

3. Vocabulary
Conditional Statement: a logical statement that has a hypothesis and a conclusion.
If-then form: format for a conditional statement.
Hypothesis: the “if” part
Conclusion: the “then” part
Hypothesis must always be true.

5. Definition
Symbols
A conditional is a statement that can be written in the form "If p, then q."
p  q
Period 3

6. Example 1: p q If it is raining, then there are clouds in the sky.
If the car is a Mustang, then it is a Ford. q p

7. Writing Conditional Statements
All birds have feathers.
Two angles are supplementary if they are a linear pair.
If an animal is a bird, then it has feathers.
If two angles are a linear pair, then they are supplementary.

8. More Examples: Rewrite as conditional statements
All 90° angles are right angles.
When n = 9, n² = 81.
Tourists at the Alamo are in Texas.
If an angle is 90, then it is a right angle
If n = 9, then n^2 = 81.
If tourists are at the Alamo, then they
are in Texas.

9. Writing a Conditional Statement
Write a conditional statement from the following.
If an animal is a blue jay, then it is a bird.
The inner oval represents the hypothesis, and the outer oval represents the conclusion.

10. Negation: the opposite of the original statement.
The ball is red.
Negation:
The cat is not black. ~p
The ball is not red. p ~p
The cat is black.
p  ~p

11. Definition
Symbols
The converse is the statement formed by exchanging the hypothesis and conclusion.
q  p

12. Converse: flip-flop the hypothesis and conclusion.
pq
If it is raining, then I will carry an umbrella.
Converse:
If I am in Nutley, then I’m in New Jersey.
qp
If I carry an umbrella, then
it is raining.
pq
qp
If I’m in New Jersey, then I am
in Nutley.
** The converse is not always true **

13. Definition
Symbols
The inverse is the statement formed by negating the hypothesis and conclusion.
~p  ~q

14. Inverse: Negate both the hypothesis and conclusion
pq
If it is a Corvette, then it is a Chevy.
Inverse:
If you are a soccer player, then you are an athlete.
~p~ q
If it is not a Corvette, then it is
not a Chevy.
pq
If you are not a soccer player,
then you are not an athlete.
~p~q
** The inverse is not always true **

15. Definition
Symbols
The contrapositive is the statement formed by both exchanging and negating the hypothesis and conclusion.
~q  ~p

16. Contrapositive: negate and flip-flop the hypothesis and conclusion.
Converse:
Inverse:
Contrapositive: F
Angle A could be ANY degree b/w F
If angle A is not 99 and it’s 100, then it IS obstuse T
Are these statements true?

17. Conditional: If an animal is a whale, then it is a mammal.
Write the conditional, converse, inverse, and contrapositive for the conditional statement: All whales are mammals
Conditional: If an animal is a whale, then it is a mammal.
Converse: If it is a mammal, then it is a whale.
Inverse: If it is not a whale, then it is not a mammal.
Contrapositive: If it is not a mammal, then it is not a whale.

18. Verifying Statements
You must show the conclusion is true every time the hypothesis is true.
It only takes one counterexample to show it’s false.

19. Use “Guitar players are musicians.” to write the following.
“If-then”
Converse
Inverse
Contrapositive
Which statements are true? Give a counterexample if it is false.

20. Equivalent Statements: when two statements are both true or false.
Conditional Statements and the contrapositive are either both true or false.
Converse and inverse are either both true or false.

21. Biconditional Statement: When a “If-Then” and its converse are true you can write them as a single statement.
Example:
Perpendicular lines: If the angle measure is 90◦, then then it is a right angle.
Converse: If the angle is a right angle, then the its measure is 90◦.
Biconditional: An angle is a right angle if and only if the its measure is 90◦

22. If Mary is in theater class, she will be in the fall play
If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater class.
Biconditional: Mary is in the fall play, if and only if she is taking a theater class.

23. HW
# 7-15, 19-21, 25, 33, 35