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I'm working on negations and there's a certain sentence I've negated which Fitch tells me is incorrect, but I can't see why, so I thought I'd get some second opinions. Here's the problem and my attempt at a solution.

Find a sentence tautologically equivalent to the negation of following:

A → (B ↔ ¬C)

Step 1: Notice that (B ↔ ¬C) is tautologically equivalent to ¬B ∨ ¬C

Step 2: Notice that ¬B ∨ ¬C is tautologically equivalent to ¬(C ∧ B)

Step 3: Substitute above sentence into first sentence, getting A → ¬(C ∧ B)

Step 4: The negation of this is equal to A → (C ∧ B)

Is this correct? If not, then why not?

Joa
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    I don't believe you are negating the implication correctly. The negation of "A implies B" is "A and not B". https://math.stackexchange.com/questions/2417770/what-is-the-negation-of-the-implication-statement – 79037662 Mar 17 '21 at 19:54
  • Ah, got it. Thanks. – Joa Mar 17 '21 at 20:21
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    Also, $B\leftrightarrow\lnot C$ is not equivalent to $\lnot B\lor\lnot C$. $$\begin{align}B\leftrightarrow\lnot C&\equiv (B\land\lnot C)\lor(\lnot B\land C)\&\equiv (B\lor C)\land(\lnot B\lor\lnot C)\end{align}$$ – Graham Kemp Mar 18 '21 at 01:05

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