SOLUTION: how to proof the arguments: 1. T ⊃ G 2. S ⊃ G ∴ (T ∨ S) ⊃ G

Algebra.Com
Question 824313: how to proof the arguments:
1. T ⊃ G
2. S ⊃ G
∴ (T ∨ S) ⊃ G
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
1. T ⊃ G
2. S ⊃ G 
∴ (T ∨ S) ⊃ G

(T ⊃ G) & (S ⊃ G)       given 
(~T ∨ G) & (~S ∨ G)     by  P ⊃ Q  <=> ~P ∨ Q
(~T & ~S) ∨ G           by ∨ is distributive over &
~(T ∨ S) ∨ G            by deMorgan's law.
(T ∨ S) ⊃ G             by  P ⊃ Q  <=> ~P ∨ Q

Edwin
RELATED QUESTIONS

INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. (answered by jim_thompson5910)
COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF Premises: 1. G ⊃ (E... (answered by robertb)
Still having issues on proofs 1.(A⊃S)⊃G 2. A⊃Q 3. G⊃B 4.... (answered by t0hierry)
COMPLETE THE FOLLOWING PROOFS WITHOUT USING CONDITIONAL PROOF OR INDIRECT PROOF... (answered by robertb)
1.(SvT)⊃ (S⊃~T) 2.(S⊃~T) ⊃ (T⊃K) 3.SvT... (answered by jim_thompson5910)
Indirect proof 9. 1) R 2) (~ C v ~ D) v S 3) ~ (C ⋅ D) ⊃ ~R / ∴ S (answered by solver91311)
Could you please help me? Im sick with a bug and cant think straight :/ A) 1. A ⊃ (answered by solver91311)
Use an ordinary proof to solve 1) 1.E ⊃ (S ⊃ T) 2.(~L ⋅... (answered by richwmiller,jim_thompson5910)
Use an ordinary proof to solve 1) 1.E ⊃ (S ⊃ T) 2.(~L ⋅... (answered by richwmiller,jim_thompson5910)