Translating English to Symbolic Logic - Multiple Quantifiers

Question

Any hints on translating this English sentence into symbolic logic:

Something is between everything.

Answer 1

Here is a quick list of rule of thumbs for translation:

• "Some" means $\exists x$
• "Every" and "All" mean $\forall x$
• "If x then y" or "x implies y" or "y only if x" mean $x\rightarrow y$
• "Either x, or y" means $x\lor y$
• "Both x and y" means $x\land y$
• "Not x" means $\lnot x$

The actual predicates you would have to fill in on your own.

As joriki and Gadi commented, "Between" is a trinary predicate (i.e. takes three variables, "x is between y and z") and the closest interpretation of the current sentence would be $\exists x\forall y\forall z\operatorname{Between}(x,y,z)$.

(Note the difference in the order I put the quantifiers and joriki put them, in his version between every two elements there is a third; in my version one specific element is between every two others, including itself.)