# SOLUTION: I need help finishing this proof. (~K -> K) -> ~L, ~(~L -> ~M) -> L, M :. K <-> ~L 1. (~K -> K) -> ~L 2. ~(~L -> ~M) -> L 3. M

Algebra ->  Algebra  -> Proofs -> SOLUTION: I need help finishing this proof. (~K -> K) -> ~L, ~(~L -> ~M) -> L, M :. K <-> ~L 1. (~K -> K) -> ~L 2. ~(~L -> ~M) -> L 3. M      Log On

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 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Proofs Question 196024: I need help finishing this proof. (~K -> K) -> ~L, ~(~L -> ~M) -> L, M :. K <-> ~L 1. (~K -> K) -> ~L 2. ~(~L -> ~M) -> L 3. MAnswer by jim_thompson5910(28715)   (Show Source): You can put this solution on YOUR website!```1. (~K -> K) -> ~L 2. ~(~L -> ~M) -> L 3. M :. K <-> ~L -------------------------- 4. (~~K v K) -> ~L 1 Material Implication 5. (K v K) -> ~L 4 Double Negation 6. K -> ~L 5 Tautology ----- 7. ~~(~L -> ~M) v L 2 Material Implication 8. (~L -> ~M) v L 7 Double Negation 9. (~~L v ~M) v L 8 Material Implication 10. (L v ~M) v L 9 Double Negation 11. L v (L v ~M) 10 Commutation 12. (L v L) v ~M 11 Association 13. L v ~M 12 Tautology 14. ~M v L 13 Commutation 15. M -> L 14 Material Implication ----- 16. M v K 3 Addition 17. K v M 16 Commutation 18. ~~K v M 17 Double Negation 19. ~K -> M 18 Material Implication 20. ~K -> L 19,15 Hypothetical Syllogism 21. ~L -> ~~K 20 Transposition 22. ~L -> K 21 Double Negation 23. (K -> ~L) . (~L -> K) 6,22 Conjunction 24. K <-> ~L 23 Material Equivalence ```