# Tagged Questions

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### Show that if n is an integer and 3n+ 2 is even, then n is even using contradiction

Show that if $n$ is an integer and $3n+ 2$ is even, then $n$ is even, using a proof by contradiction. That's the question. So since we're using contradiction, I need to show that N is odd and prove ...
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### If $x\rightarrow y$ and $y \rightarrow z$, prove, by contradiction, that $x \rightarrow z$

Say you're given $$x\Rightarrow y$$ $$y\Rightarrow z$$ Prove that $x\Rightarrow z$ by contradiction. It seems like such a simple task, because it's easy to evaluate that it must be true. But I ...
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### logic: two simple math contradictions

1.The contradiction of the sentence: - There is a greater number than a million. can be stated as follows: - There is a number which is not greater than a million. 2.and the contradiction of the ...
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Let's say I attempted to solve a logical statement in the form using contradiction: $\forall x \in \Bbb R, (P \implies Q)$ Negated: $\exists x \in \Bbb R, (P \land \lnot$ Q). Initially I did not ...
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### Does a proof by contradiction always exist?

Good day, Usually, proofs by contradictions are the easier, and sometimes, even the only ones available. However, there are cases where the easiest proof is not the proof by contradiction. For ...
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### How to solve a statement with contradiction evidence?

I'm trying to solve the statement below with contradiction evidence. If $(P \rightarrow Q)$ and $(Q \rightarrow R)$ is true, then $(P \rightarrow R)$ is true. This is what i've done so far: ...
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### What practical proofs work in intuitionistic but not minimal logic?

Intuitionistic logic contains the rule $\bot \rightarrow \phi$ for every $\phi$. In the formulations I have seen this is a separate axiom, and the logic without this axiom(?) is termed "minimal ...
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### Is my proof that $(p \wedge \neg p) \Rightarrow q$ correct?

I was asked by a professor a while ago to prove $(p \wedge \neg p)$ implies $q$. Whether through laziness or cleverness, I came up with the following proof: $p \wedge \neg p$ (by assumption). ...
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### help me define the connectives for 3 value logic

so basically i have a project about 3 valued logic ie truth=1 false = 0, unknown = 1/2 in a previous project I had to come up with formulae for 2 valued logic as follows: ...
Classical logic has the theorem ($p\wedge\lnot p)\rightarrow q$, which I will call EFQ ("ex falso quodlibet"). Constructive logic often has the principle built in, in the form of an axiom ...