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) Q(y,x)) is satisfied in this model if, and only if, for all values of x we can find a value for y such that the pair (x,y) or the pair (y,x) is in QM. Thus, we need to verify this for all possible choices of x. Thus, the last case demonstrated that, given that x has value d, the disjunction Q(x,y) Q(y,x) is false for all values of y. Therefore, the formula in question is not satisfied in the given model.
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