1. Goal 1: Using Symbolic Notation Goal 2: Using the Laws of Logic
2.3 Deductive Reasoning
CAS 1, 3
Goal 1: Using Symbolic Notation
Goal 2: Using the Laws of Logic

2. Symbolic Notation
Conditional statements can be written using symbolic notation.
The letter “p” represents the hypothesis.
The letter “q” represents the conclusion.

3. How P and Q is Used
If the A’s lose against the Angels, then they will not go to the playoffs.
To identify the hypothesis and conclusion, you can use p and q instead of the words: Hypothesis and Conclusion.
p: The A’s lose against the Angels
q: They will not go to the playoffs

4. Other Ways Symbolic Notation is Used
Original statement: If the A’s lose against the Angels, then they will not go to the playoffs.
(Converse)
If the A’s do not go to the playoffs, then they lost against the Angels.
(Inverse)
If the A’s do not lose against the Angels, then they will go to the playoffs.
(Contrapositive)
If the A’s do go to the playoffs, then they did not lose against the Angels.

5. Other Ways Symbolic Notation is Used continued~
Biconditional Statement.
The A’s lose against the Angels if and only if they go to the playoffs.

6. Deductive vs. Inductive Reasoning
Deductive Reasoning uses facts, definitions, and accepted properties in a logical order to write a logical argument.
Inductive Reasoning uses previous examples and patterns to form a conjecture.
See example 3 p. 89

7. Deductive Reasoning Deductive Reasoning has two laws
The Law of Detachment
The Law of Syllogism

8. Law of Detachment
If is a true conditional statement and p is true, then q is true.
Ex. 2 Conditional Statement:
If Alex goes to the store, then she will buy popcorn.
Using Deductive Reasoning, more specifically, the Law of Detachment, if we know that Alex went to the store, then we can deduce that Alex will buy popcorn.

9. The Law of Syllogism
If and are true conditional statements, then is true.
Ex. 3 If Ryan talks too much, then Megan will throw the ball. If Megan throws the ball, then the batter will be out.
Using Deductive Reasoning, more specifically, the Law of Syllogism, one can deduce that if Ryan talks too much then the batter will be out.