Correct Answer.


The formula set { x y P(x,y), x P(x,x)} is satisfied in a model M, if all the formulas in that set are satisfied by that same model. Thus, we seek a model, M, that satisfies the two formulas The first formula states that P is a "total" relation: for all values a, there has to be some value b such that (a,b) is in PM. The second formula says that no pair of the form (a,a) can be in PM. With these constraints at hand, we can easily construct a model M that satisfies both formulas:

A = {a,b};
PM = {(a,b),(b,a)}.


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