Translate the following sentences to FOL:
1)Mary loves all fluffy cats 2)Anybody who trusts nobody deceives themself. 3)Tom's uncle does not like any of his own children.
From my understanding of First-order logic I have come to these answers:
1) ∀x[cat(x) ^ fluffy(x) loves(Mary,x)]
2) ∀x[Person(x) trusts(x, ¬ x) deceives(x, x)]
3)This third one has been bugging me for quite some time now. I have come to 4 answers and I am not sure wether one of these is correct or if there is a correct one at all:
a) ∃x∀y ¬[Uncle(x,Tom) Child(y) ^ likes(x,y)]
b) ∃x∀y [Uncle(x,Tom) Child(y) ^ ¬ likes(x,y)]
c) ∃x∀y ¬[Uncle(x,Tom) Child(y,x) ^ likes(x,y)]
d) ∃x∀y [Uncle(x, Tom) Child(y,x) ^ ¬ likes(x,y)]
On c) and d) I write "Uncle - Child" relation the same way as "Uncle - Tom" (not sure if it is correct)
If you could explain where I am wrong and right and why I would much appreciate it. Thank you!