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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. 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)
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.
/:.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
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.
/:.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