1. 2.1 Conditional Statements
Objective: To recognize and write converses of conditional statements.

2. Conditional Statement
A logical statement with 2 parts
2 parts are called the hypothesis & conclusion
Can be written in “if-then” form; such as, “If…, then…”
Hypothesis is the part after the word “If”
Conclusion is the part after the word “then”

3. Ex 1: Underline the hypothesis & circle the conclusion.
If you are a brunette, then you have brown hair.
hypothesis conclusion
Ex 2: Underline the hypothesis & circle the conclusion.
If a polygon has 6 sides, then it is a hexagon.
hypothesis conclusion

4. Ex 3: Rewrite the statement in “if-then” form
Vertical angles are congruent.
If 2 angles are vertical, then they are congruent.
An object weighs one ton if it weighs 2000 lbs.
If an object weighs 2000 lbs, then it weighs one ton.

5. Counterexample Used to show a conditional statement is false.
It must keep the hypothesis true, but the conclusion false!

6. Ex 4: Find a counterexample to prove the statement is false.
If x2=81, then x must equal 9.
counterexample: x could be -9
because (-9)2=81, but x≠9.
Ex 5: Find a counterexample to prove the statement is false.
If you live in Virginia, then you live in Richmond.
Counterexample:
I live in Virginia, BUT I live in Glen Allen.

7. Converse
Switch the hypothesis & conclusion parts of a conditional statement.
Ex 6: Write the converse of “If you are a brunette, then you have brown hair.”
If you have brown hair, then you are a brunette.

8. Ex 7: Converse State the converse of the if-then statement:
If a polygon has five sides, then it is a pentagon.
Converse: If a polygon is a pentagon, then it has five sides.
True or False?
True
Truth Value

9. Symbolic Logic is used to represent p  q
Symbols can be used to modify or connect statements.
Symbols for Hypothesis and Conclusion:
Hypothesis is represented by “p”.
Conclusion is represented by “q”.
if p, then q or
p implies q
p  q
is used to represent

10. Conditional Statements and Converses
                                                                                                                                                                                                                                                

11. Assignment
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