Question 1010045: can i have help solving these proofs
a regular proof to derive the conclusion of the following argument:
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
a regular proof to derive the conclusion of the following argument:
1. N > R
2. O <> R
3. (O > R) > L / (N > O) & L
a regular proof to derive the conclusion of the following argument:
1. H v (~T > R)
2. Hv (E > F)
3. ~T v E
4. ~H & D / R v F
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first two to get you started
# 1
| Number | Statement | Lines Used | Reason |
|---|
| 1 | C | | | | 2 | (C & T) -> ~T | | | | 3 | (C & ~T) -> T | | | | :. | T <--> ~T | | | | 4 | C -> (T -> ~T) | 2 | Exportation | | 5 | C -> (~T -> T) | 3 | Exportation | | 6 | (T -> ~T) | 4,1 | Modus Ponens | | 7 | (~T -> T) | 5,1 | Modus Ponens | | 8 | (T -> ~T) & (~T -> T) | 6,7 | Conjunction | | 9 | T <--> ~T | 8 | Material Equivalence |
# 2
| Number | Statement | Lines Used | Reason |
|---|
| 1 | N -> R | | | | 2 | O <--> R | | | | 3 | (O -> R) -> L | | | | :. | (N -> O) & L | | | | 4 | (O -> R) & (R -> O) | 2 | Material Equivalence | | 5 | (R -> O) & (O -> R) | 4 | Commutation | | 6 | R -> O | 5 | Simplification | | 7 | N -> O | 1,6 | Hypothetical Syllogism | | 8 | O -> R | 4 | Simplification | | 9 | L | 3,8 | Modus Ponens | | 10 | (N -> O) & L | 7,9 | Conjunction |
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