1. Chapter 2 Deductive Reasoning
Proving statements by reasoning from accepted postulates, definitions, theorems, and given information.

2. 2-1 If – then statements; Converses
A) Terms
1) If – then statements or conditional statements.
Ex. If it is raining, then it is Monday.
hypothesis conclusion
a) Symbol: p: hypothesis
q: conclusion
Ex. If p, then q. (p → q)

3. Ex. Statement: Elephants are grey.
Conditional statement:
If an animal is an elephant, then it is grey.
Ex. Statement: A catfish is a fish that has no scales.
If a fish is a catfish, then it has no scales.

4. 2) Converse statements
is reversing the hypothesis and conclusion of a conditional statement.
a) symbol: If q, then p. (q → p)
Ex. Converse:
If an animal is grey, then it is an elephant.
Ex. Converse:
If a fish has no scales, then it is a catfish.
*Some converse statements are false based on the conditional statement.

5. 3) Counterexample
is an example that proves an if – then statement is false.
*It takes only one counterexample to prove something is false.
Ex. If Sue lives in Pennsylvania, then she lives in Reading.
Counterexample: She could live in Allentown or any other city in Pennsylvania.

6. B) Different ways an if, then form can be written.
1) If p, then q ex. If x = 3, then 6x = 18
2) p implies q x = 3 implies 6x = 18
3) p only if q x = 3 only if 6x = 18
4) q if p x = 18 if x = 3