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Which of the below first order logic formulae represent the sentence

There is a student who is loved by every other student

Here, $\text{Loves}(x,y)$ means $x$ loves $y$

  1. $\exists x (\text{Student} (x) \wedge \forall y (\text{Student} (y) \wedge \neg (x=y) \rightarrow \text{Loves} (y,x))) $
  2. $\exists x (\text{Student} (x) \rightarrow  \forall y (\text{Student} (y) \wedge \neg (x=y) \wedge \text{Loves} (y,x))) $
  3. $\exists x (\text{Student} (x) \wedge \forall y (\text{Student} (y) \wedge \neg (x=y) \vee \text{Loves} (y,x))) $
  4. $\exists x (\text{Student} (x) \wedge \forall y (\text{Student} (y) \to \neg (x=y) \rightarrow \text{Loves} (y,x))) $
asked in Mathematical Logic by Boss (15.3k points)
edited by | 103 views
+1
Is it A
+3
options A and D are same...

Someone plz correct it...
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where are the answers for these questions ?

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