Are these translations correct?
Translate the following sentences into wfs.
- a) Nobody loves a loser.
Let $H(x,y):= x$ loves $y$.
Then $\lnot(\exists x\exists p (H(x,p)))$
- b) Nobody in the statistics class is smarter than everyone in the logic class.
(which is the same (I think) as 'All in the logic class are smarter than all in the statistic class.')
Let H(x,y):=x is smarter than y, p(x)=x is in the logic class and q(x)=x is in the statistic class.
Then $\forall x\forall y[(q(y)\land p(x))\to H(x,y)]$
- c)Anyone who knows Julia loves her.
(This is the same as 'If x knows Julia, then x loves Julia.')
Let $p(x)=x $ knows Julia, H(x,J)=x loves Julia.
Then $\forall x(p(x)\to H(x,J))$
- d) There is no set belonging to precisely those sets that do not belong to themselves.
Let $H(x,y)=$The set x belongs to the set y.
Then $\forall\forall[\lnot H(x,y)\land \lnot H(y,y)]$
- e) There is no barber who shaves precisely those men who do not shave themselves.
Let H(x,y)=x shaves y.
Then $\forall x\forall y[\lnot H(x,y)\land \lnot H(y,y)]$