Some apples are red, but not any red apple is green


Ax : An object is an Apple

Rx : An object is red

Gx : An object is green

I have assigned the "but" in the question to the logical Operater ∧, so I wrote this:

∀x(∃x(Ax ∧ Rx) ∧ ∀x((Ax ∧ Rx) → -Gx))

Which I think reads as: For any X, There is at least one object that is an apple and is red, and for any x, If an object is an apple and is red, then the object is not green.

Is this correct?

  • $\begingroup$ This makes sense! $\endgroup$ – Peter Oct 17 '17 at 18:30
  • $\begingroup$ Not sure if sarcasm but I edited my question to make more sense. @peter $\endgroup$ – MattyS11 Oct 17 '17 at 18:35
  • $\begingroup$ This was not meant sarcastic. $\endgroup$ – Peter Oct 17 '17 at 18:35
  • 3
    $\begingroup$ The outer ∀x is not needed. $\endgroup$ – Mauro ALLEGRANZA Oct 17 '17 at 18:54

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