1 / 13

Aim 1.5: To explore proofs and the Laws of Logic

Aim 1.5: To explore proofs and the Laws of Logic. Do Now: Logic Quiz Homework: Packet pages 7 & 8. Proofs:. Proofs can be written in two ways: In a two column Statement – Reason form With p’s and q’s ( or other variables ) Valid proofs will always include a given and a conclusion .

dolph
Download Presentation

Aim 1.5: To explore proofs and the Laws of 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 1.5: To explore proofs and the Laws of Logic Do Now: Logic Quiz Homework: Packet pages 7 & 8

  2. Proofs: • Proofs can be written in two ways: • In a two column Statement – Reason form • With p’s and q’s ( or other variables ) • Valid proofs will always include a given and a conclusion. Aim 1.5: To explore proofs and the Laws of Logic

  3. Example: Given: After school Sam either went to the park or went home. Sam did not go home. Conclusion: Therefore Sam went to the park Aim 1.5: To explore proofs and the Laws of Logic

  4. Example: Given: Mike can choose between pizza or pasta for lunch. Mike did not eat pasta for lunch. Conclusion: Therefore Mike ate pizza for lunch. Aim 1.5: To explore proofs and the Laws of Logic

  5. Aim 1.5: To explore proofs and the Laws of Logic Law of Disjunctive Inference: LODI • LODI allows us to draw a conclusion between two statements using a disjunction. • One statement is a disjunction and the other is a negation of one of the disjuncts. • Our conclusion will be the remaining p or q • A proof is only valid when there is a negation of p or q

  6. Law of Disjunctive Inference: LODI Given: Mike can choose between pizza or pasta for lunch. Mike did not eat pasta for lunch. Conclusion: Mike did eat pizza for lunch. Let p represent Mike ate pizza Let q represent Mike at pasta p V q Given “If p or q is true” ~q Given “q is not true” p LODI “therefore p is true” Aim 1.5: To explore proofs and the Laws of Logic

  7. Law of Disjunctive Inference: LODI Given: Mike can choose between pizza or pasta for lunch. Mike did not eat pasta for lunch. Conclusion: Mike did eat pizza for lunch. Statement Reason 1. Mike can choose between 1. Given pizza or pasta for lunch. 2. Mike did not eat pasta 2. Given for lunch. 3. Mike ate pizza for lunch 2. LODI 1, 2 Aim 1.5: To explore proofs and the Laws of Logic

  8. Example: Given:If today is Thursday, then I have practice after school Today is Thursday Conclusion: Therefore I have practice after school Aim 1.5: To explore proofs and the Laws of Logic

  9. Example: Given: If I studied last night I will pass the test I studied last night Conclusion: Therefore I will pass the test Aim 1.5: To explore proofs and the Laws of Logic

  10. Aim 1.5: To explore proofs and the Laws of Logic Law of Detachment • The law of detachment says that when two statements are true, the conclusion of the conditional will also be true. • If the hypothesis false, then our proof will be invalid. We cannot determine the truth value of our conclusion.

  11. Law of Detachment Given: If today is Thursday, then I have practice after school Today is Thursday Conclusion: Therefore I have practice after school Let p represent “today is Thursday” Let q represent “I have practice after school” p  q Given “If p implies q” p Given “and p is true” q Law of Detachment “therefore q is true” Aim 1.5: To explore proofs and the Laws of Logic

  12. The laws of logic are not tied to particular letters ~r  t ~r t Aim 1.5: To explore proofs and the Laws of Logic

  13. Law of Detachment Given: If today is Thursday, then I have practice after school Today is Thursday Conclusion: Therefore I have practice after school Statement Reason • If today is Thursday, then I 1. Given have practice after school • Today is Thursday 2. Given • Therefore I have practice 3. Law of Detachment 1,2 after school. Aim 1.5: To explore proofs and the Laws of Logic

More Related