I'm kind of confused on whether or not these sentences are correct or not (particularly on something being sufficient for an argument to be true vs. something being necessary)


a = alice

b = bob

Lxy = x loves y

Fxy = x fears y

  1. Bob doesn't fear anyone, $\forall x \neg Fbx$

  2. Everyone who loves bob fears bob, $\forall x (Lxb \rightarrow Fxb)$

    • (not sure if the antecedent and consequent should be flipped)
  3. No one who fears alice fears bob, $\forall x (\neg Fxa \rightarrow Fxb)$

  4. If anyone loves alice, then alice loves herself, $\exists x (Lxa \rightarrow Laa)$



The first two seems to be right.

(3) should be$\forall x (Fxa \rightarrow \neg Fxb)$

(4) $\exists x Lxa \rightarrow Laa$ (the quantifier should act only over the antecedent)

  • $\begingroup$ Hi, Could you please elaborate on the meaning of 3)? I don't quite understand. $\endgroup$ – JC1 Oct 17 '16 at 3:03
  • $\begingroup$ Sure. "No one who fears alice fears bob" is equivalent to saying "any person who fears alice does not fear bob", right? (English is not my native language, so I might be wrong, correct me in that case), and that would be the translation to predicate logic I wrote above. The way you wrote it means "anybody who does not fear alice fears bob" $\endgroup$ – la flaca Oct 17 '16 at 3:09
  • $\begingroup$ Was a bit confused on the original sentence - thanks for breaking it down for me $\endgroup$ – JC1 Oct 17 '16 at 3:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.