Incorrect Answer.


Given the predicate logic model

A = {a,b,c,d};
PM = {a,b}
QM = {(a,b), (b,b), (c,b)}
fM (a) = b, fM (b) = b, fM (c) = a, and fM (d) = c

the formula x y (Q(x,y) P(x)) is satisfied in this model if, and only if, for all values of x and y such that the pair (x,y) is in QM we also have that x is in PM. To determine whether this formula is satisfied in the given model, we only have to verify the validity of the implication for all choices of x and y, where (x,y) is in QM (why?). Thus, the last case demonstrated that the implication Q(x,y) P(x) does not hold for all choices of x and y. Therefore, the formula in question is not satisfied in the given model.
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