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R(x) is a red block
B(x) is a blue block
T(x,y) block x is on top of block y
Question:
Write 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
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”).