# translation into predicate logic

• Jan 15th 2012, 07:23 AM
Sea90
translation into predicate logic
Hello,

I am in need of some help with translating the following sentences into predicate logic.

1. Exept for Jean, all mathematicians travelled to Egypt.
2. Some mathematicians don't take the conversations seriously when not everyone is present.
3. At least one mathematician wants to speak with Jean and Jean alone.

So I was thinking for 1) Ax (M(x) > (~(x=y)> E(x)) whereas M(x) means that x is a mathematician and E(x) x travelled to Egypt.

2) Ex~Ay (M(x) & (P(y) > ~S(x)) whereas P(x) means that x is present and S(x) means that x takes the conversations seriously.

3) Ex (M(x) & T(x,j)) whereas T(x,y) means that x wants to speak with y and with y alone.

I am not realy sure about 3. Is there another way to tell that x wants to speak with y and y alone? I need to be sure these sentences are correct.

Thanks!
• Jan 15th 2012, 08:24 AM
ILikeSerena
Re: translation into predicate logic
Welcome to MHF, Sea90! :)

I would interpret the statement "wants to speak with Jean and Jean alone" as "wants to speak with Jean and does not want to speak with anyone else".
• Jan 15th 2012, 08:42 AM
Sea90
Re: translation into predicate logic
Thanks for the welcome!

I think you are rigtht about the third,
will this be a better translation?

Ex (M(x) & S(x,j) & Ay (~(y=j) > ~S(x,y))) Whereas S(x) means x wants to talk with y.
• Jan 15th 2012, 08:43 AM
ILikeSerena
Re: translation into predicate logic
Quote:

Originally Posted by Sea90
Thanks for the welcome!

I think you are rigtht about the third,
will this be a better translation?

Ex (M(x) & S(x,j) & Ay (~(y=j) > ~S(x,y))) Whereas S(x) means x wants to talk with y.

Looks fine to me.
• Nov 1st 2012, 04:30 AM
jpatel3
Re: translation into predicate logic
Hey Guys,

I Am In Need Of Some Help With Translating The Following Sentences Into Predicate Logic.

1. Jessica Cannot Outrun Any Man On The Team.
2. Jessica Cannot Outrun Every Man On The Team.
3. Everybody Knows Somebody Who Knows Alice.
4. Somebody Knows Everybody Who Knows Bob.

Cheers... :)
• Nov 1st 2012, 06:57 AM
emakarov
Re: translation into predicate logic
Quote:

Originally Posted by jpatel3
I Am In Need Of Some Help With Translating The Following Sentences Into Predicate Logic.

1. Jessica Cannot Outrun Any Man On The Team.
2. Jessica Cannot Outrun Every Man On The Team.
3. Everybody Knows Somebody Who Knows Alice.
4. Somebody Knows Everybody Who Knows Bob.

You should start a new thread with this problem in the same subforum. Also, you should make an attempt to solve the problem and describe your difficulties. At least come up with predicate symbols and constants that should be used in the translation (hint: mnemonic names are preferable).