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could someone explain to me why the sentence - There are exactly two purple mushrooms is represented in FOL like this:

(Ex)(Ey) mushroom(x) ^ purple(x) ^ mushroom(y) ^ purple(y) ^ ~(x=y) ^ (Az) (mushroom(z) ^ purple(z)) => ((x=z) v (y=z))

especially the last part i have problem with. i assume that i misunderstood some of the definitions which are the basis of FOL, that might be the source of the confusion.

thanks for your help

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# First order logic

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