Fill This Form To Receive Instant Help

Help in Homework
trustpilot ratings
google ratings


Homework answers / question archive / Question 1 10 pts Determine whether the following argument is valid or invalid

Question 1 10 pts Determine whether the following argument is valid or invalid

Philosophy

Question 1 10 pts Determine whether the following argument is valid or invalid. If the argument is invalid, upload a counterexample world. If it is valid, please upload an informal proof of the conclusion from the premises. 1. Larger(a, b) 2. Small(a) v Medium(b) 1..Large(a) Upload Choose a File Question 2 10 pts Determine whether the following argument is valid or invalid. If the argument is invalid, upload a counterexample world. If it is valid, please upload an informal proof of the conclusion from the premises. 1. Between(a, b, c) 2. Same Row (a, c) 3. LeftOfic, a) 7.Leftof(a,b) ABackOf(b,a)

pur-new-sol

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE

Answer Preview

Question 1

Determine whether the following argument is valid or invalid. If the argument is invalid, upload a counterexample world. if it is valid, please upload an informal proof of the conclusion from the premises.

  1. Larger (a, b)
  2. Small(a) v Medium(b)

/:.larger(a)

Proof

Valid

(Small (a) Smaller (a, b)) v (Large (b) Smaller (a, b)), c = b} |= Smaller (a, c) c = b

1. (Small (a) Smaller (a, b)) v (Large (b) Smaller (a, b))

2. c = b

3. Small (a) Smaller (a, b)

4.Smaller(a, b)                           Elim: 3

5. Large (b)        Smaller (a, b)

6. Smaller(a, b)                            Elim: 5

 7. Smaller(a, b)                          Elim: 1, 3-4. 5-6

 8. c = c Refl=

 9. b = c Ind. Id: 8, 2

 10. Smaller(a, c) Ind. Id.: 7, 9

11. Smaller(a, c) c= b Intro: 10, 2

 

 

Question 2

Determine whether the following argument is valid or invalid. If the argument is invalid, upload a counterexample world. if it is valid, please upload an informal proof of the conclusion from the premises.

  1. Between(a, b, c)
  2. LeftOf(c, a)

/:.LeftOf(a,b)BackOf(b,a)

Proof

Valid

Between (a, b, c) → {a → b, a → (b → c), b → (c → d) } |= a → d

1. a → b

2. a → (b → c)

3. a → (b → c)

 4. a [(LeftOf (c, a)]}

5. b                  →Elim: 4, 1

6. b → c                      →Elim: 4, 2

7. a → c                       →Elim: 5, 3

8. c (LeftOf(b, d))                    →Elim: 5, 6

9. a                  →Elim: 8, 7

10. a → c                     →Intro: 4-9