SOLUTION: Please help me answer this one natural proof CORRECTLY using the 8 rules of implication and 10 rules of replacement, thank you! 1. (Q•R)v(~Q•~R) 2. N>~(Q=R) 3. EvN / E

Algebra ->  Proofs -> SOLUTION: Please help me answer this one natural proof CORRECTLY using the 8 rules of implication and 10 rules of replacement, thank you! 1. (Q•R)v(~Q•~R) 2. N>~(Q=R) 3. EvN / E       Log On


   

Question 1045414: Please help me answer this one natural proof CORRECTLY using the 8 rules of implication and 10 rules of replacement, thank you! 1. (Q•R)v(~Q•~R) 2. N>~(Q=R) 3. EvN / E
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. (Q•R)v(~Q•~R) --------------hypothesis
2. (Q v (~Q•~R))•(R v (~Q•~R))-----------distributivity of v
3. (Q v ~Q)•(Q v~R)•(R v~Q)•(R v~R)------distributivity of v
4. T•(Q v~R)•(R v~Q)•T ---------------tautology
5. T•(Q v~R)•(R v~Q) ---------------idempotency of T
6. (Q v~R)•(R v~Q) ----------------simplification
7. (R > Q)•(Q > R) ----------------material implication
8. Q = R ----------------tautology
9. N>~(Q=R) ---------------hypothesis
10.(Q=R) > ~N ----------------contrapositive of #9
11. ~N ----------------modus ponens from #8 and #10
12. E v N ----------------hypothesis
13. E ----------------disjunctive syllogism from #11 and #12