# Tag Info

### The converse of Euclid lemma : counter example?

Euclid's lemma states that if $p$ is prime, then $p \mid ab$ implies $p \mid a$ or $p \mid b$. The lemma makes absolutely no comment on the case when $p$ is composite. In fact, the statement can be ...
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### Can negations be arbitrarily added to both sides of an equation?

The "first negation law" says that $\lnot \exists x P(x)$ is equivalent to $\forall x \lnot P(x)$ for every formula $P(x)$. The key word here is: every formula. We can replace $P(x)$ by any ...
• 32.7k
Accepted

### Is there a simpler Kripke counter-model for this formula?

There isn’t really a nicer model. Any model with finitely many states will fail. To see this, note that maximal elements are “dense” in the finite state case (every element is less than a maximal ...
• 30.8k
Accepted

### The definition of proposition and the principle of the excluded third

A proposition is defined as a statement or assertion that can either be true or false. Here's a more direct definition: A proposition/sentence is a string of symbols that is well-formed according to ...
• 38k
A better way to state the first definition is that a proposition is the sort of thing that is eligible to be judged true or false. That is, they are the sort of things $P$ about which it at least ...