1. Do Now : What do you believe is meant by the term “logic”? Dictionary.com defines the term “logic” as the science that investigates the principles governing correct or reliable inference. Aim : What exactly are logical proofs?

2. Logic If Something (true or false) Then Something else (true or false) Q Based on weather the first term, “P”, or the second term, “Q” is true depends on the outcome of the logical setup. P P -> Q

3. Aim : What exactly are logical proofs? Conditional Inverse Converse Contrapositive Continue To “THE RULES”

4. Using a setup similar to the one in the earlier slide Set up this phrase as terms such as “P” or “Q” P -> Q _______P_______ ∴ Q If it rains, I will need a jacket It started to rain So I took my jacket Aim : What exactly are logical proofs?

5. ~P -> ~Q If the temperature is not below 0 degrees, then it is not cold P -> Q If the temperature is below 0 degrees, then it is cold Aim : What exactly are logical proofs? Back to THE BASICS

6. Q -> P If it is Cold, then it is below 0 degrees Aim : What exactly are logical proofs? ~Q -> ~ P If it is not Cold, then it is not below 0 degrees Back to THE BASICS

7. Law of Disjunctive Inference Law of Detachment De Morgan's Law Chain Rule Law of Disjunctive AdditionLaw of Simplification Aim : What exactly are logical proofs? CONTINUE LESSON Back to THE BASICS

8. Aim : What exactly are logical proofs? Back to THE RULES P -> Q ____P___ ∴ Q If it rains, I will need a jacket It started to rain So I need my jacket P -> Q _____Q_____ ∴ P If it rains, I will need a jacket I need my jacket So it is raining

9. Aim : What exactly are logical proofs? Back to THE RULES P \/ Q _ ~Q______ ∴ P It either rained or snowed It did not snow So it rained

10. Aim : What exactly are logical proofs? Back to THE RULES ___P /\ Q___ ∴ P ___P /\ Q___ ∴ Q I read and I write So I read I read and I write So I write

11. Aim : What exactly are logical proofs? Back to THE RULES ___P___ ∴ P \/ Q I am sleeping So I am either sleeping or doing homework

12. Aim : What exactly are logical proofs? Back to THE RULES _~(~P /\ ~Q)_ ∴ P \/ Q _~(P /\ Q)_ ∴ ~P \/ ~Q _~(P \/ Q)_ ∴ ~P /\ ~Q _~(~P \/ ~Q)_ ∴ P /\ Q I like math and science ~(I like math and science) I don’t like math or I don’t like science I like math or science ~(I like math or science) I don’t like math and I don’t like science

13. Aim : What exactly are logical proofs? Back to THE RULES P -> Q _ Q -> R______ ∴ P -> R I want things If they are green If it is green, then it was made with green dye So I want things made from green dye

14. 1. Assume the statement "Michael is taking sociology and biology" is true. Which of the following statements must be true? [A] Michael is taking both sociology and biology. [B] Michael is taking neither sociology, nor biology. [C] Michael is taking only sociology. [D] Michael is taking only biology. 2. Assume the statement "Cheryl is taking fencing or sculpture" is true. Which of the following statements must be false? [A] Cheryl is taking only sculpture. [B] Cheryl is taking neither fencing, nor sculpture. [C] Cheryl is taking both fencing and sculpture. [D] Cheryl is taking only fencing. 3. Assume the statement "James is taking drama and physics" is true. Which of the following statements must be true? [A] James is taking both drama and physics. [B] James is taking only drama. [C] James is taking neither drama, nor physics. [D] James is taking only physics. 4. Assume the statement "James is taking history or tennis" is true. Which of the following statements must be false? [A] James is taking only tennis. [B] James is taking neither history, nor tennis. [C] James is taking only history. [D] James is taking both history and tennis. 5. Assume the statement "James is taking drama and physics" is true. Which of the following statements must be true? [A] James is taking both drama and physics. [B] James is taking only physics. [C] James is taking only drama. [D] James is taking neither drama, nor physics. 6. Assume the statement "Pamela is taking music or physics" is true. Which of the following statements must be false? [A] Pamela is taking only music. [B] Pamela is taking only physics. [C] Pamela is taking neither music, nor physics. [D] Pamela is taking both music and physics.

15. pq~p~qp/\qp\/qp->q ~p\/q p qp\/~p TTFFTTTTT FFFTTFFFT FTTFTFTFT FFTTFFTTT HW: Fill Out the Below Table Based on the given information Aim : What exactly are logical proofs?