1. Conditional Statements
Definition: A statement written in two parts, a hypothesis and a conclusion. When the conditional sis written in if-then form, the “if” part is the hypothesis and the “then” part is the conclusion.
Example: If today is Monday, then tomorrow is Tuesday.
“today is Monday” is the hypothesis
“tomorrow is Tuesday” is the conclusion

2. Converse
Definition: Formed by exchanging the hypothesis and conclusion.
Original: If today is Monday, then tomorrow is Tuesday.
Converse: If tomorrow is Tuesday, then today is Monday.

3. Inverse Definition: Make both the conclusion and hypothesis negative.
Original: If today is Monday, then tomorrow is Tuesday.
Inverse: If today is NOT Monday, then tomorrow is NOT Tuesday.

4. Contrapositive
Definition: The converse of the inverse. (Flip the hypothesis and conclusion and make both negative)
Original: If today is Monday, then tomorrow is Tuesday.
Contrapostive: If tomorrow is NOT Tuesday, then today is NOT Monday.

5. Format
Conditional Statement
A  B
Converse
B  A
Inverse
NOT A  NOT B
Contrapositive
NOT B  NOT A

6. Counterexample
Definition: Proof that a conditional statement could be in incorrect, in at least one instance.
Example: If Sam lives in Florida, then he must live in Orlando.
Counterexample: Sam could live in Miami.

7. Inductive Reasoning
Definition: the process of observing data, recognizing patterns, and making generalizations about those patterns.

8. Conjecture
Definition: the conclusion or generalization developed while using inductive reasoning.

9. Practice Your Inductive Reasoning Skills…
Find the next three terms in the sequence.
2, 4, 7, ___, ___, ___
1, 1, 2, 3, 5, 8, ____, ____, ____
8, 11, 15, 20, ____, _____, _____
5, 25, 125, ____, _____, _____