logic - Converting Normal Form to CNF -

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in cs logic class have convert normal form boolean expressions cnf, kind of stuck on one.

¬(¬p => (p => q))

which is:

¬(¬p => (¬p or q)) implication elimination

¬(¬¬p or (¬p or q)) implication elimination

¬(p or (¬p or q)) double negation

¬p , ¬(¬p or q)) demorgan's

¬p , (¬¬p , ¬q)) demorgan's

¬p , (p , ¬q)) double negation

the next step distribute or on and, there aren't or distribute.

once reach

  • ¬(p or (¬p or q)) double negation

you have

  • ¬((p or ¬p) or (p or q)) distribution
  • ¬(true or (p or q)) excluded middle
  • ¬(true) null element of or
  • false obviousness :p

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