SOLUTION: Use rules of implication to derive the indicated conclusions.
1. R ⊃ (G v ~A) 2. (G v ~A) ⊃ ~S 3. G ⊃ S 4. R/~A
1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B
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Question 1201675: Use rules of implication to derive the indicated conclusions.
1. R ⊃ (G v ~A) 2. (G v ~A) ⊃ ~S 3. G ⊃ S 4. R/~A
1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D
1. ~M ⊃ Q 2. R ⊃ ~T 3. ~M v R / Q v ~T
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
I'll do problem 1 to get you started.
This is what the 1st question looks like when each premise gets its own line.
1. R ⊃ (G v ~A)
2. (G v ~A) ⊃ ~S
3. G ⊃ S
4. R
:. ~A
Here is one way to do the derivation.
| Number | Statement | Lines Used | Reason |
| 1 | R -> (G v ~A) | | |
| 2 | (G v ~A) -> ~S | | |
| 3 | G -> S | | |
| 4 | R | | |
| :. | ~A | | |
| 5 | R -> ~S | 1,2 | Hypothetical Syllogism |
| 6 | ~S | 5,4 | Modus Ponens |
| 7 | G v ~A | 1,4 | Modus Ponens |
| 8 | ~G | 3,6 | Modus Tollens |
| 9 | ~A | 7,8 | Disjunctive Syllogism |
I used arrows in place of the horseshoe symbols.
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/
Similar logic questions
https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.1198762.html
https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.1193810.html
https://www.algebra.com/algebra/homework/Proofs/Proofs.faq.question.1194113.html
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