SOLUTION: Hi, how do I solve these two Proofs?
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Question 1207463: Hi, how do I solve these two Proofs?
https://ibb.co/r5XF5dS
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Problem 5
I'll use an arrow symbol in place of the horseshoe symbol.
| Number | Statement | Line(s) Used | Reason |
| 1 | F --> ~U | | |
| 2 | ~F --> P | | |
| 3 | F v ~F | | |
| :. | ~U v P | | |
| 4 | ~~U --> ~F | 1 | Transposition |
| 5 | U --> ~F | 4 | Double Negation |
| 6 | U --> P | 5,2 | Hypothetical Syllogism |
| 7 | ~U v P | 6 | Material Implication |
Note: A much quicker pathway is to use the Constructive Dilemma rule.
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Problem 6
| Number | Statement | Line(s) Used | Reason |
| 1 | (J v F) v M | | |
| 2 | (J v M) --> ~P | | |
| 3 | ~F | | |
| :. | ~(F v P) | | |
| 4 | (F v J) v M | 1 | Commutation |
| 5 | F v (J v M) | 4 | Associative |
| 6 | J v M | 5,3 | Disjunctive Syllogism |
| 7 | ~P | 2,6 | Modus Ponens |
| 8 | ~F & ~P | 3,7 | Conjunction |
| 9 | ~(F v P) | 8 | De Morgan’s Law |
The Rules of Inference and Rules of Replacement are shown here
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