# SOLUTION: ~(A or B) or ~(C or D) (E or F) -> D therefore A-> ~E

Algebra ->  Algebra  -> Proofs -> SOLUTION: ~(A or B) or ~(C or D) (E or F) -> D therefore A-> ~E      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

 Question 189186: ~(A or B) or ~(C or D) (E or F) -> D therefore A-> ~EAnswer by jim_thompson5910(28595)   (Show Source): You can put this solution on YOUR website!Note: I'm going to use the symbol "v" for "or" So ~(A or B) = ~(A v B) ```1. ~(A v B) v ~(C v D) 2. (E v F) -> D / A -> ~E ------------------------------- 3. (~A & ~B) v (~C & ~D) 1 De Morgan's Law 4. [(~A & ~B) v ~C] & [(~A & ~B) v ~D] 3 Distribution 5. [(~A & ~B) v ~D] & [(~A & ~B) v ~C] 4 Commutation 6. (~A & ~B) v ~D 5 Simplification 7. ~D v (~A & ~B) 6 Commutation 8. (~D v ~A) & (~D v ~B) 7 Distribution 9. ~D v ~A 8 Simplification 10. ~A v ~D 9 Commutation 11. A -> ~D 10 Material Implication 12. ~(E v F) v D 2 Material Implication 13. (~E & ~F) v D 12 De Morgan's Law 14. D v (~E & ~F) 13 Commutation 15. (D v ~E) & (D v ~F) 14 Distribution 16. D v ~E 15 Simplification 17. ~~D v ~E 16 Double Negation 18. ~D -> ~E 17 Material Implication 19. A -> ~E 11,18 Hypothetical Syllogism ```