1
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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)

Let:

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, $\exists x (Lxa \rightarrow Laa)$

Thanks

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3
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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)

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  • $\begingroup$ 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

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