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
- x Q(x)
- x (Q(x) R(x)) and
- x R(x).
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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