# Logic - if and only iff

• Mar 17th 2009, 10:46 AM
sabatier
Logic - if and only iff
Hi, could anyone tell me how I would write this sentence
in first order logic:

"Bob likes to chase any animal if and only if Tom doesn't like
to chase that animal."

Bob and Tom are constants. Use the predicate L(x,y) for
"x likes to chase y".

Any help appreciated,

sabatier
• Mar 17th 2009, 10:52 AM
wytiaz
b <--> !t
• Mar 17th 2009, 10:54 AM
sabatier
Hi, thanks for your reply. I should have mentioned
to use the predicate L(x,y) for "x likes to chase y".

Regards,

sabatier
• Mar 17th 2009, 11:08 AM
Plato
On the universe of animals: $\left( {\forall x} \right)\left[ {L(B,x) \Leftrightarrow \neg L(T,x)} \right]$ .