Question 1150092: 1. [A v (K & J)] > (~E &~F)
2. M > [A & (P v R)]
3. M & U /~E & A
How do I continue?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The conclusion has ~E and A. So we'll have to track down those terms.
We see "A" is buried in the second premise. To free it, we need to use modus ponens. So we'll need the antecedent M. Luckily line 3 has an M we need. Use the simplification rule to go from M&U to just M. We will never use the "U" that is part of line 3. This is likely a distraction your teacher has thrown in.
Once we have M, we can use modus ponens along with line 2 to get A & (P v R). Use simplification to reduce that to just A. The (P v R) is never used. Probably another distraction.
With "A" freed up, we can use the addition rule to add on any logical expression we want. Go from A to A v (K & J). This builds up the antecedent of premise 1, which helps free up ~E & ~F
Now use simplification yet again to get ~E.
Together with ~E and A, we'll use the conjunction rule to get the conclusion we are aiming for.
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Here's what the full derivation looks like
| Number | Statement | Line(s) Used | Reason |
| 1 | [A v (K & J)] > (~E & F) | | |
| 2 | M > [A & (P v R)] | | |
| 3 | M & U | | |
| :. | ~E & A | | |
| 4 | M | 3 | Simp |
| 5 | A & (P v R) | 2,4 | MP |
| 6 | A | 5 | Simp |
| 7 | A v (K & J) | 6 | Add |
| 8 | ~E & F | 1,7 | MP |
| 9 | ~E | 8 | Simp |
| 10 | ~E & A | 9,6 | Conj |
Abbreviations Used:
Add = Addition
Conj = Conjunction
MP = Modus Ponens
Simp = Simplification
The rules of addition, conjunction, modus ponens and simplification are part of a group of logic rules of inference.
For more information, check out the link below
https://www2.cs.duke.edu/courses/summer13/compsci230/restricted/lectures/L05.pdf
(the specific rules are found on pages 5, 9, 10, and 11)
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