# Logical translation for 'at most' using FOL

Only using existential and universal quantifiers, I am trying to translate the following sentence:

"At most b and c are large cubes."

Please express the properties 'large' and 'cube' using the following atomic predicates Large(a) and Cube(a).

Any hints would be appreciated!

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"If something is a large cube, then it is b or c." – Andrés Caicedo May 4 '11 at 6:23
I don't know if it helps but its equivalent to "If $x\neq y$ are large cubes, then $\{x,y\}=\{b,c\}$" so you would not have the nasty "at most" – Listing May 4 '11 at 6:25

## 1 Answer

Hint: For all $x$, if large($x$) and cube($x$) then $x=b$ or $x=c$.

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At most, means at least one correct? – KerxPhilo May 4 '11 at 6:47
As far as I read it, at most means that if there are any there cannot be more than two. – Asaf Karagila May 4 '11 at 6:50