1. Warm Up
For this conditional statement: If a polygon has 3 sides, then it is a triangle.
Write the converse, the inverse, the contrapositive, and the biconditional forms:
Converse:
Inverse:
Contrapositive:
Biconditional :

2. Inductive and Deductive Reasoning
Chapter 2.2

3. Conjectures and Inductive Reasoning
(Topic video)
Conjecture: an unproven statement that is based on observations
Inductive Reasoning: what you use when you find a pattern in a specific case and then make a conjecture for the general case (like the brown mice).

4. Inductive Reasoning and Counterexamples
Counterexample: a specific case for which the conjecture is false. To show that a conjecture is true, it must be true for ALL cases!
Example of a counterexample:
conjecture: The sum of two numbers is always more than the bigger number.
4+5 = 9 This would make the conjecture true because 9 > 5
This is a counterexample
-4+(-5) = -9 The conjecture is false because -9 is NOT greater than -4

5. Deductive Reasoning
Deductive Reasoning: uses facts and the laws of logic to form an argument. There are 2 laws of logic:
1) Law of Detachment: If a conditional statement is true, and the hypothesis (p) is true, then the conclusion (q) must also be true.
True statement!
Example: If I miss my bus, I will be late to school.
p is true
I missed my bus.
therefore…..
q is true
I will be late to school.

6. Inductive and Deductive Reasoning
(Topic video)
Law of Syllogism:
It’s like the transitive property of equality in algebra: if A=B and B=C then A=C
If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If hypothesis p, then conclusion r.
If these statements are true,
Then this statement is true.
Example
If I get to the Café late, then I will not have time to eat lunch.
If I do not have time to eat lunch then I will be hungry.
If I get to the Café late, then I will be hungry.