# I am stuck on this homework question (Formal Logic class w/ Fitch) my proofs are messed up in the end. I need to start over, but that is what i have

I think my main issue is understanding if I am translating the negation of the statement correctly. I feel as if it is ultimately not logical when negated. Can someone please translate the first line please?

Exercise 6 . 3 7 . In the following exercise, assess whether the indicated sentence is a logical truth in the blocks language. If so , use Fitch to construct a formal proof of the sentence from no premises ( using Ana Con if necessary, but only applied to literals ) . If not, use Tarski ’ s World to construct a counterexample. ( A counterexample here will simply be a world that makes the purported conclusion

• Do you think the sentence is always true or not? Mar 10 at 5:37
• That is not a logical truth, so there is no point trying to prove it. If a is Eminem, b is Taylor Swift and c is Slim Shady, then you have a counterexample. Mar 10 at 16:32
• Isn't it true that 0 ≠ 1 AND 1 ≠ 0 AND 0 = 0? i.e. whenever c ≠ b, let c = a, and we have that the given statement is false. Mar 11 at 20:37
• Thank you all for your help and advice. I was able to see how it is not logical and create a counter example in tarski's. I really appreciate everyone's time on responding Mar 13 at 23:02

Cogito ...

(A = B) ∨(B = C) ∨¬(A = C)

Where do you see this kinda statement?
Re cogito .... There are at most 2 (whatever).
∀x∀y∀z((Gx ⋀ Gy ⋀ Gz) ⊃ (x = y) ⋁ (y = z) ⋁ (x = z))

If you want to say at least 2 (whatever) then,
∀x∀y∀z((Gx ⋀ Gy) ⊃ (x ≠ y))

• Thank you so much for your response. Mar 13 at 23:03
• You're welcome @mechesad24. Mar 14 at 1:17