Translating sentence into symbols

[Nathew]

I'm having trouble with translating this english sentence into logic symbols.

The sentence is

The numbers four and five aren't both prime, but the numbers five and seven are.

I was thinking ~(F&I)v(IvS) but I really don't know how to deal with the "but".

Thanks

 

[jedishrfu]

How about just using and?

 

[Nathew]

so
~(F&I)&(I&S)
?

 

[jedishrfu]

I meant the upside down v commonly used in logic for AND. The v itself is used for OR.

 

[TeethWhitener]

I was thinking ~(F&I)v(IvS) but I really don't know how to deal with the "but".

Jedishrfu is exactly right. In logic, "but" is equivalent to "and." If you say, for example "x is A but y is B," what you're really saying is "x is A and y is B," and the "but" merely points out that there is some sort of contrast that you want draw the listener's attention to.