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
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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
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