1. DRILL
What would be the coordinates of the point (-2, 4) if it was reflected over the y-axis?
If you dilate the point (-3, 9) using a scale factor of 1/3, then what would be the coordinates of the new point?
If Angle A is 2x + 4 and Angle B is x + 16, given they are supplementary then what is the measure of Angle A?

2. 4.1 Logical Reasoning
Objective: Today, we will write and interpret different types of conditional statements.

3. Vocabulary
Conditional Statement: any statement that follows the form “If”…“then”….
Hypothesis: the statement that follows the “If”.
Conclusion: the statement that follows the “then”.
EX: If you pass the final, then you will pass the class.

4. Vocabulary
Biconditional Statement: any statement that follows the form ….“if and only if”….
*This only works when a conditional statement and its converse are both true.
Ex: You will graduate from college if and only if you have a passing test average in all of your classes.

5. Conditional Statement
Any statement in the form if “P” then “Q”.
Read: “P implies Q”
If “hypothesis”, then “conclusion”
Ex: All cars are red.
If it is a car, then it is red.

6. Identify the hypothesis and the conclusion in each statement.
If an animal meows, then it is a cat.
If you drive very fast, then you will get a ticket.

7. Negations
A negation is just when we say the opposite of our statement.
Ex: The car is red.
Negation: The car is not red.
Ex: I failed the test.
Negation: I passed the test.
Symbol: The symbol for a negation is ~p.
Read as “not p”

8. Vocabulary
Converse: When the If and then statements are switched around.
“the hypothesis and conclusion change places”.
Inverse: negates both the hypothesis and conclusion.
Contrapositive: Interchanges the statements and negates both of them.

9. A Closer Look at If-Then Statements
Symbolism:
Conditional Statements p  q
Converse Statements q  p
Inverse Statements ~p  ~q
Contrapositive Statements ~q  ~p
* A “If”, “then” statement is only False, when a True  False (True Implies False)

10. Homework
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