# Tagged Questions

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### Laws of equivalence

Need to proof using laws $$\lnot(p \land \lnot q) \lor q \equiv \lnot p \lor q$$ $\lnot(p \land \lnot q) \lor q$ $\equiv (\lnot p \lor \lnot(\lnot q)) \lor q\quad$ First De Morgan's law ...
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### My proof is wrong, can anyone tell me why?

$$\forall x \in \mathbb{Z}, \forall y \in \mathbb{Z}, [x(x+1) = y(y+1)] \Leftrightarrow [x = y]$$ $$\forall x \in \mathbb{Z} , \forall y \in \mathbb{Z}, [x(x+1)=y(y+1)]\Leftrightarrow [x=y]$$ ...
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### Countable transitive $T \vDash ZFC-P$ with $\approx$ not absolute: why do we need $H(\aleph_3)$?

I am trying to solve Exercise IV.3.31 from Kunen's Foundations of Mathematics. I think I have a solution but I am confused by one of the hints. By request, here is the text of the exercise. ...
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### Valid argument form for knaves problem (spoilers)

I would like to know if my argument is valid for the following problem. Another two natives C and D approach you but only C speaks. C says: Both of us are knaves. What are C and D? My solution is as ...
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### Proof of Drinker paradox [duplicate]

I searched all over the internet but didn't find a formal proof for this paradox, so here is my attempt: $\exists x[P(x)\implies \forall yP(y)]$ Let $x=x_0$. Thus $P(x_0)$ is given. Let $y$ be ...
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### Logical fallacy?

Suppose I have two mathematical statements : $A$ and $B$. Suppose that $A$ is an already proven theorem. Suppose that, to prove $B$, I use $A$ somewhere in the proof. Therefore, $B$ is a proven ...
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### Logic Proof with Natural Deduction: if I assume the antecedent, do I still have to prove the consequent?

I have the unpleasent feeling that my "proof" is dead wrong. The core of my concerns is: when I have something like A -> (B -> C) and I assumed ...
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### Question about Logic Proof

Assuming $P$ is a unary predicate and $Q$ is a propositional variable, I'm trying to prove the following implication: $$(\forall x (P(x)\rightarrow Q)\rightarrow ((\forall x P(x) )\rightarrow Q)$$ ...
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### Construct the truth table?

Any body help me .. How to solve this? (i) $(p\land q)\to (p \leftrightarrow (q \lor r))$ (ii) $(p \leftrightarrow q) \leftrightarrow ((p\land q) \lor (\neg q \land \neg p))$ (iii) ...
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### Proving ∀x (0|x ↔ x = 0) (divisor by Zero) - Euclidean Algorithm

I am trying to proof the total correction of Euclidean Algorithm, so I am up to proof one of the following properties which is divisor by Zero. Given this Axiom: ...
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### The unique model of cardinal $\kappa$ of a $\kappa$-categorical countable theory is saturated.

Let $T$ be a $\kappa$-categorical ($\kappa \geq \aleph_1$) first-order theory in a countable language $\mathcal L$. I try to prove that its unique (up to isomorphism) model of cardinal $\kappa$ is ...