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Day 3 Logic math Notes, Slides of Mathematics

Mathematics

Learns the five rules, which are HS, LA, DS, DP, CL

Typology: Slides

2017/2018

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August 18, 2016
Day 3 : Logic
5 Rules: HS, LA, DS, DP, CL
Quick review:
Symbolize and identify the sentence:
a) It is raining or it is sunny, and I am tired.
b) Either I am wrong and question number one
is true or question number two is true.
Reminder : Quiz on Day 1 next week!!
RVS AT
who VT
pf3
pf4
pf5
pf8
pf9
pfa

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Download Day 3 Logic math Notes and more Slides Mathematics in PDF only on Docsity!

Day 3 : Logic

5 Rules: HS, LA, DS, DP, CL

Quick review: Symbolize and identify the sentence: a) It is raining or it is sunny, and I am tired. b) Either I am wrong and question number one is true or question number two is true. Reminder : Quiz on Day 1 next week!! RVS AT who (^) VT

Warm Up Prove: A. B Given: 1. A. C 1. Premise

  1. ~C / D 2. Premise
  2. E โ†’ ~D 3. Premise
  3. (F / B) / E 4. Premise
  4. ~F 5. Premise

Law of Addition (LA): Recall: Disjunction P / Q...... Given as a premise.... What must be true? P, or Q, (or both P and Q) must be true. What can you conclude? I am a student Premise (given, true) I am a student or I am a lawyer True I am a student or pigs can fly!! True Note: only 1 must be true!! Law of Addition (LA) - as long as one part of the disjunction is true, then the whole statement is true. The Rule in Symbols: see example below: Ex: Prove S / T

  1. ~T โ†’ A 1. Premise
  2. ~A 2. Premise
  3. T 3. TT ( 1 , 2 )
  4. S / T 4. LA ( 3 ) (Note- S is not mentioned in the premises. "Poof" like magic it appears. Remember only one part of a disjunction must be true for the whole statement to be true.

LAW OF DISJUNCTIVE SYLLOGISM (DS) Given: Either it is raining or it is sunny. P / Q If it is raining, then we stay indoors. P โ†’ R If it is sunny, then we go outside. Q โ†’ S Symbolized: 1. P / Q

  1. P โ†’ R
  2. Q โ†’ S What can we conclude? Either we stay inside or we go outside.
  3. R / S DS ( 1 , 2 , 3 ) LAW OF DISJUNCTIVE SIMPLIFICATION (DP) Given: T / T Conclusion: T / T T (DP) When is it ever used?
  4. P / Q P
  5. P โ†’ R P
  6. Q โ†’ R P
  7. R / R DS ( 1 , 2 , 3 )
  8. R DP ( 4 )

Practice Time !!!!!! Practice Makes Perfect! Practice Problem # 1 Prove: ~A / B

  1. C โ†’ D 1. Premise
  2. E / ~A 2. Premise
  3. E โ†’ ~(F โ†’D) 3. Premise
  4. F โ†’ C 4. Premise
  5. F โ†’ D 5. HS ( 1 , 4 )
  6. ~E 6. TT ( 3 , 5 )
  7. ~A 7. TP ( 2 , 6 )
  8. ~A / B 8. LA ( 7 ) Note: B is not mentioned in the premises.. What law do you think you might need to use somewhere in the proof?? HS 1 4 Fit FAA NAUB (^) WA 7

Practice # 2

Prove: P / Q

1. ~R โ†’ S 1. Premise

2. (T โ†’S) โ†’ W 2. Premise

3. ~W / P 3. Premise

4. T โ†’ ~R 4. Premise

5. T โ†’ S 5. HS ( 1 , 4 )

6. W 6. PP ( 2 , 6 )

7. P 7. TP ( 3 , 6 )

8. P / Q 8. LA ( 7 )

White Board Time.... Which Law: soooooo FN For PUG LA 7 AVB TP TT

Which Law: Which Law: S pp

Which Law: Which Law: HS DP