SOLUTION: Prove that the following two arguments are valid using the method of Natural Deduction. Show your work, which means “do the proofs just like Hurley does them.” Note that ‘//’ is

Algebra ->  Proofs -> SOLUTION: Prove that the following two arguments are valid using the method of Natural Deduction. Show your work, which means “do the proofs just like Hurley does them.” Note that ‘//’ is       Log On


   

Question 1050201: Prove that the following two arguments are valid using the method of Natural Deduction. Show your work, which means “do the proofs just like Hurley does them.” Note that ‘//’ is used as a conclusion indicator.

1. (R & I)
2. [(R v G) -> Z] // (Z v ~W)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. (R v G) -> Z ------------------hypothesis
2. ~(RvG) v Z --------------------material implication
3. (~R ^ ~G) vZ ------------------de Morgan's
4. (~RvZ)^(~GvZ) ------------------distributivity
5. ~R v Z ------------------------simplification
6. R -> Z ------------------------material implication
7. R ^ I -------------------------hypothesis
8. R -----------------------------simplification
9. Z -----------------------------modus ponens on #6 and #8
10. Z v ~W -----------------------addition property of v