SOLUTION: 1. D 2. ~C 3. (A v B) -> C 4. [(~A • D) • ~B] -> (P -> Q) :. ~P v Q

Algebra.Com
Question 616557: 1. D
2. ~C
3. (A v B) -> C
4. [(~A • D) • ~B] -> (P -> Q) :. ~P v Q
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
1. D
2. ~C
3. (A v B) -> C 
4. [(~A • D) • ~B] -> (P -> Q) :. ~P v Q
-------------------------------------------------------
6. ~(A v B)                                    3,2      Modus Tollens
7. ~A • ~B                                     6        De Morgan's Law
8. (~A • ~B) • D                               7,1      Conjunction
9. ~A • (~B • D)                               8        Association
10. ~A • (D • ~B)                              9        Commutation
11. (~A • D) • ~B                              10       Association
12. P -> Q                                     4,11     Modus Ponens
13. ~P v Q                                     12       Material Implication


RELATED QUESTIONS

Hi there, I'd love some help on answering these Logic Proof Questions: 1. 1. T > O (answered by math_tutor2020)
If vector x is denoted by V(x), If v(d)=p(V(a)XV(b))+q(V(b)XV(c))+r(V(c)XV(a)) and... (answered by venugopalramana)
1. (P v F) -> (A v D) 2. A -> (M ^ ~P) 3. D -> (C ^ ~P) /... (answered by Edwin McCravy)
Prove: Q (1) [~(A•C)->Q]•Z (2) [~B v ~(A•C)]•D (3)`B->Q (4) (5) (6)... (answered by solver91311)
1. A -> (B -> C) 2. A -> B 3. ~ C ->(A V D) / C V... (answered by Edwin McCravy)
1. ~ A V (B & E) 2. ~ A -> ~ C 3. C V (B & D) /... (answered by Edwin McCravy)
1. (A v B) > ~C 2. C v D 3. A Conclusion: D (answered by jim_thompson5910)
1. A v (B v C) 2. C ⊃ (D • E) 3. ~D / A v B (answered by mccravyedwin)
I need help finishing this proof. A v (~B v ~C), A -> (D -> E), ~(~B v ~D) :. C -> (D -> (answered by jim_thompson5910)