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

Algebra ->  Proofs -> 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      Log On


   

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) About Me  (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.
NumberStatementLines UsedReason
1R -> (G v ~A)
2(G v ~A) -> ~S
3G -> S
4R
:.~A
5R -> ~S1,2Hypothetical Syllogism
6~S5,4Modus Ponens
7G v ~A1,4Modus Ponens
8~G3,6Modus Tollens
9~A7,8Disjunctive 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/

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