Logic Web Tutor: Wrong Answer

Incorrect Answer.

The formula set {

x Q(x),

Q(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

x Q(x) and
x Q(x).

For the first formula to be satisfied in M, we need a value a for x such that a is in Q^M. But the latter makes it impossible for M to satisfy the second formula, which states (if re-expressed with quantifier equivalences) that no value a is in Q^M.

Thus, there cannot be a model M that satisfies both formulas. (Can you find models that satisfy one of these formulas?)

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