1. Conditional Statements
Lesson 2.2
Conditional
Statements

2. Conditional Statement
A conditional statement is _______________
_____________________________________
Definition:
____ your feet smell and your nose runs, _______ you're built upside down.
Example:

3. Conditional Statement - continued
Conditional Statements have ______ parts:
The hypothesis is the part of a conditional statement that follows _______ (when written in if-then form.)
The hypothesis is _________________________________.
The conclusion is the part of an if-then statement that follows ________ (when written in if-then form.)
The conclusion is ______________________________.

4. Writing Conditional Statements
Conditional statements can be written in ________form to emphasize which part is the hypothesis and which is the conclusion.
Hint: Turn the _________ into the hypothesis.
Example 1:
Vertical angles are congruent.
can be written as...
Conditional Statement:
____________________________________________.
Example 2:
Seals swim.
can be written as...
Conditional Statement:
____________________________________________.

5. Two angles are vertical __________they are congruent.
If …Then vs. Implies
Another way of writing an if-then statement is using the word _______________.
If two angles are vertical, then they are congruent.
Two angles are vertical __________they are congruent.

6. Conditional Statements can be true or false:
A conditional statement is FALSE only when ________________
____________________________________________________.
A counterexample is an example used to show that a statement is _______________________________________________________.
Statement:
If you live in Virginia, then you live in Richmond.
Is there a counterexample?
____________
Counterexample:
________________________________________.
Therefore () the statement is _________.

7. Symbolic Logic
Symbols can be used to ________________________________.
Symbols for Hypothesis and Conclusion:
Hypothesis is represented by “____”.
Conclusion is represented by “____”.
if ____, then _____ or
____ implies ____

8. Symbolic Logic - continued
_______________ or _______________
________
is used to represent
Example:
p: a number is prime
q: a number has exactly two divisors
pq:
______________________________________________

9. is used to represent the word
Symbolic Logic - continued
____
is used to represent the word
“______”
Example 1:
p: the angle is obtuse
~p:
_____________________________________
Note:
~p means that the angle could be acute, right, or straight.
Example 2:
p: I am not happy
~p:
_________________________________________
~p took the “not” out; it would have been a double negative (not not)

10. is used to represent the word
Symbolic Logic - continued
_______
is used to represent the word
“_______”
Example:
p: a number is even
q: a number is divisible by 3
pq:
________________________________________.
i.e. _________________________________

11. is used to represent the word
Symbolic Logic- continued
________
“_____”
is used to represent the word
Example:
p: a number is even
q: a number is divisible by 3
pq:
_______________________________________.
i.e. __________________________________

12. is used to represent the word
Symbolic Logic - continued
_______
is used to represent the word
“____________”
Example:
Therefore, the statement is false.
_______________________________

13. Forms of Conditional Statements
Converse: _____________the hypothesis and conclusion (p  q becomes ____________)
Conditional:
pq If two angles are vertical, then they are congruent.
Converse:
_______ ________________________________________.

14. Forms of Conditional Statements
Inverse: State the __________ (or _____________) of both the hypothesis and conclusion. (p  q becomes __________)
Conditional:
pq : If two angles are vertical, then they are congruent.
Inverse:
______ _____________________________________.

15. Forms of Conditional Statements
Contrapositive: __________the hypothesis and conclusion and state the ____________. (p  q becomes ____________)
Conditional:
pq : If two angles are vertical, then they are congruent.
Contrapositive:
_______ ___________________________________.

16. Forms of Conditional Statements
Contrapositives are _____________________________
_____________________________________________
If pq is true, then qp is _______.
If pq is false, then qp is _______.

17. Biconditional
When a conditional statement and its converse are both true, ____ _____________________________________________________.
Use the phrase ________________ (sometimes abbreviated: ____)
Statement: If an angle is right then it has a measure of 90.
Converse: If an angle measures 90, then it is a right angle.
Biconditional: ___________________________________________.