# Tag Info

### Why does the AND take precedence over OR in most programming languages?

From a mathematic point of view, the right structure is the Boolean semiring $\mathbb{B}$, not the field $\mathbb{F}_2$. Recall that a commutative semiring is a set $R$ equipped with two binary ...
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### Proof that $\left<B,f,\cup \right>$ is a Boolean Algebra

You've shown that for all $y$ we have $y\cap y''=y''$, taking $y=x'$ we have $x'''=x'\cap x'''$, therefore:  x\cap x'''=x\cap (x'\cap x''')=(x\cap x')\cap x'''=(x''\cap x''')\cap x'''=x''\cap (x'''\...
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Accepted

### Finite Boolean combinations of rational intervals, as a subspace of $\{0,1\}^{\mathbb{R}}$: is it $C^*$-embedded?

(I asked a related question on MathOverflow, to which I recieved an answer by KP Hart with references to a paper by Engelking and Pełczyński which is used as inspiration in the following direct answer ...
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### All proofs are equal for Boolean algebras

If you study those definitions more precisely, you may see more clearly that some of the inferences you draw are not true. A Boolean algebra is commonly regarded as a lattice. The well-formed formulae ...

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