1. Warmup
Write the two conditionals(conditional and converse) that make up this biconditional:
An angle is acute if and only if its measure is between 0 and 90.

2. Go over hmwk

3. 2.3 Deductive Reasoning
10/4

4. Learning Target
I can draw conclusions using the Law of Detachment and the Law of Syllogism

5. Remember inductive reasoning is based on observing and making a conjecture
Deductive Reasoning: Reasoning logically from given statements to a true conclusion. Reasoning based on facts.

6. Law of Detachment: If a conditional is true and its hypothesis is true, then its conclusion is true.
If p  q is a true statement and p is true, then q is true.

7. Law of Detachment
An auto mechanic knows that if a car has a dead battery, then the car will not start.
The mechanic works on the car and finds the battery is dead.
What can the mechanic conclude?
Law of Detachment says, if the conditional is true (is it?) and the hypothesis is true (is it?), then the conclusion is true.

8. Is the conditional true?, is the hypothesis true?
Using Law of Detachment
Given: If M is the midpoint of a segment, then it divides the segment into two congruent parts
M is the midpoint of segment AB, what can you conclude using the Law of Detachment?
Is the conditional true?, is the hypothesis true?

9. Given: If a road is icy, then driving conditions are hazardous.
What can you conclude using the Law of Detachment?
Is the conditional true? Is the hypothesis true?

10. Law of Syllogism: allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement
If pq and qr are true statements, then pr is a true statement

11. If a number is prime, then it does not have repeated factors.
If a number does not have repeated factors, then it is not a perfect square.
Here you have two true conditional statements and the conclusion of one is the hypothesis of the other. So we can also say
If a number is prime, then it is not a perfect square.

12. If a number ends in 0, then it is divisible by 10.
If a number is divisible by 10, then it is divisible by 5.
What can you conclude using the Law of Syllogism?

13. If a number ends in 6, then it is divisible by 2.
What can you conclude using the Law of Syllogism?

14. Homework
1-3 in Packet
#1-12

15. Homework
P #1-13 all,22,24,25