Logical translation for 'at most' using FOL

Question

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!

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 04 '11 at 06:25

score 7 · Accepted Answer · answered May 04 '11 at 06:33

7

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

answered May 04 '11 at 06:33

Asaf Karagila

At most, means at least one correct? – Philoxopher May 04 '11 at 06:47
As far as I read it, at most means that if there are any there cannot be more than two. – Asaf Karagila May 04 '11 at 06:50

1 Answers1