Logic Web Tutor: Wrong Answer

Incorrect Answer.

Given the predicate logic model

A = {a,b,c,d};
P^M = {a,b}
Q^M = {(a,b), (b,b), (c,b)}
f^M (a) = b, f^M (b) = b, f^M (c) = a, and f^M (d) = c

the formula

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 Q^M we also have that x is in P^M. 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 Q^M (why?).

If the value of x is a and the value of y is b, then a is in P^M.
If the value of x is b and the value of y is b as well, then b is in P^M.
If the value of x is c and the value of y is b, then c is not in P^M.

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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