Incorrect Answer.


The formula set { x Q(x), x (Q(x) R(x)), x R(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 three formulas For the first formula to be satisfied in M, we need a value a for x such that a is in QM. But if the second formula is satisfied in M, this implies that a is also in RM. The latter makes it impossible for M to satisfy the third formula, which states (if re-expressed with quantifier equivalences) that no value of M is in RM.

Thus, there cannot be a model M that satisfies all three formulas. (Choosing any two formulas above, can you find models that satisfy these two formulas?)
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