Incorrect Answer.


The formula set { x Q(x), 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 For the first formula to be satisfied in M, we need a value a for x such that a is in QM. 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 QM.

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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