I have two compound propositions:

  1. $(A \land B)$
  2. $\neg (A \rightarrow \neg B)$

I know they are equivalent, because I made their truth tables, however I'm still running into a problem when I use logical equivalences.

I tried applying the Implication Law to number 2 and obtained: $\neg ((\neg A) \lor (B))$ Then I applied De Morgans law and obtained: $(A \land (\neg B))$

Clearly those two compound proposition are not equivalent. Am I doing something wrong?

  • 3
    $\begingroup$ obtained: not((not A) or (B)) Check this step more carefully. You should actually obtain $\lnot(\lnot A \lor \lnot B)\,$. $\endgroup$ – dxiv Jan 24 '17 at 1:49
  • 1
    $\begingroup$ Thank you, I found my mistake! $\endgroup$ – cicero866 Jan 24 '17 at 2:02

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