SOLUTION: CREATE A PROOF FOLLOWING THE ARGUMENT
(F • ~C) ⊃ (G • ~C)
C ⊃ D
~D
F ∨ D /G
Algebra.Com
Question 1194046: CREATE A PROOF FOLLOWING THE ARGUMENT
(F • ~C) ⊃ (G • ~C)
C ⊃ D
~D
F ∨ D /G
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
This is one way (of possibly many) to do the derivation.
| Number | Statement | Line(s) Used | Reason |
| 1 | (F & ~C) -> (G & ~C) | | |
| 2 | C -> D | | |
| 3 | ~D | | |
| 4 | F v D | | |
| :. | G | | |
| 5 | F | 4, 3 | Disjunctive Syllogism |
| 6 | ~C | 2, 3 | Modus Tollens |
| 7 | F & ~C | 5, 6 | Conjunction |
| 8 | G & ~C | 1, 7 | Modus Ponens |
| 9 | G | 8 | Simplification |
For more information, check out the various rules of inference and rules of replacement as shown in the link below.
https://logiccurriculum.com/2019/02/09/rules-for-proofs/
RELATED QUESTIONS
Use the first eight implication rules to create a proof of the following argument.
1. B... (answered by Edwin McCravy)
Use Indirect Proof to solve the following argument
(E v F) ⊃ (C • D)
(D v G) ⊃ (answered by jim_thompson5910,Edwin McCravy)
B ⊃ ∼C
C ∨ [D ∨ (G • K)]
∼G ∨ ∼K
B ⊃ D
Create a method for the... (answered by mccravyedwin)
Create a proof for the following argument.
1.~D
2.B ⊃ (C ⊃ D) /~(B •... (answered by math_tutor2020)
C/d+2=f/g
(answered by Alan3354)
• U = {a, b, c, d, e, f, g, h, i, j, k}
• A = {a, c, d, f, g, i}
• B = {b, c, d, f,... (answered by stanbon)
Determine the following: B ∪ C if:
U= {a, b, c, d, e, f, g, h, I, (answered by jim_thompson5910)
a-{b-[c-(d-e)-f]-g} (answered by Mathtut)
CREATE A PROOF FOLLOWING THE ARGUMENT
K ∨ L
(K ⊃ F) • (R ⊃ S)
(N ⊃ K) •... (answered by Edwin McCravy)