First order logic formula

R(x) is a red block

B(x) is a blue block

T(x,y) block x is on top of block y

Question:

W开发者_StackOverflowrite a formula asserting that if no red block is on top of a red block then no red block is on top of itself.

My answer: (Ax)(Ay)(R(x) and R(y) -> ~T(x,y))->(Ax)(R(x)-> ~T(x,x))

A = For all

~ = Not

-> = implies

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That is a plausible formulation, though not necessarily the most straight-forward translation of the sentence, which, to my mind, is (Ax)(Ay)(T(x,y) -> R(x) -> ~R(y)) -> ~(3x)(R(x) and T(x,x)). 3, here, being the existential quantifier (i.e. "there exists an").

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Looks good to me.

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(Ax)(Ay)(Az) { (((R(x) and R(y)) -> ~T(x,y)) -> ~T(z,z) }