1 / 16

Do Now : What do you believe is meant by the term “logic”?

Aim : What exactly are logical proofs?. 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. Logic. P -> Q. P. If Something (true or false)

berke
Download Presentation

Do Now : What do you believe is meant by the term “logic”?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Aim : What exactly are logical proofs? 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.

  2. Logic P -> Q • P 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. SO IN ORDER FOR "SOMETHING" TO HAPPEN A DIFFERENT "SOMETHING" MUST FIRST HAPPEN

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

  4. Aim : What exactly are logical proofs? 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

  5. ~P -> ~Q If the temperature isnotbelow 0 degrees, then it isnotcold Aim : What exactly are logical proofs? Conditional P -> Q If the temperature is below 0 degrees, then it is cold Inverse Back to THE BASICS

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

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

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

  9. Aim : What exactly are logical proofs? Law of Disjunctive Inference P\/Q _ ~Q______ ∴ P It eitherrainedorsnowed It did not snow So it rained Back to THE RULES

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

  11. Aim : What exactly are logical proofs? Law of Disjunctive Addition ___P___ ∴ P\/Q I am sleeping So I am eithersleeping ordoing homework Back to THE RULES

  12. Aim : What exactly are logical proofs? De Morgan's Law _~(~P/\~Q)_ ∴ P\/Q _~(P/\ Q)_ ∴ ~P\/~Q I like mathand science ~(I like mathandscience) I don’tlike mathor I don’t like science _~(P\/Q)_ ∴ ~P /\ ~Q _~(~P\/~Q)_ ∴ P/\Q I like mathorscience ~(I like mathorscience) I don’tlike mathand I don’t like science Back to THE RULES

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

  14. 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. 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. AND I DID REALIZE THAT THEY WERE ALL DETATCHMENT

  15. Aim : What exactly are logical proofs? HW: Fill Out the Below Table Based on the given information

More Related