This is an interactive website to help you learn how to write a logic proof. You should try to write the proof yourself, and use the information on this webpage to check your work or to get a hint if you need one.

You will write similar proofs in your homework. You can see that most of the proof is missing, as are the rules used in the proof. Click on the empty boxes to reveal the steps.

But before you click, try to write the proof yourself and figure out what will appear! Keep in mind that there may be other valid proofs, and your work does not have to match up line-by-line with what you find on this page.

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 $$1.\ (L\vee M)\vee (N\cdot O)$$ $$2.\ (\sim L\cdot O)\cdot \sim(\sim L\cdot M)$$ $$\therefore \sim L \cdot N$$ $$3.\ \sim L\cdot (O\cdot \sim(\sim L\cdot M))$$ 2 Assoc. $$4.\ \sim L$$ 3 Simp. $$5.\ L\vee (M\vee (N\cdot O))$$ 1 Assoc. $$6.\ M\vee (N\cdot O)$$ 4, 5 DS $$7.\ (M\vee N)\cdot (M\vee O)$$ 6 Dist. $$8.\ M \vee N$$ 7 Simp. $$9.\ \sim L \cdot (M\vee N)$$ 4, 8 Conj. $$10.\ (\sim L \cdot M)\vee (\sim L \cdot N)$$ 9 Dist. $$11.\ \sim(\sim L \cdot M)$$ 2 Comm., Simp. $$12.\ \sim L \cdot N$$ 10, 11 DS