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Suppose a problem statement is :

In a school, supposeS(x)is“x is a student”,F(x)is“x is a faculty member”andA (x, y)is“x asked a question to y”. Domain is all the people associated with the school. Write the following using quantifiers:

"Some student did not ask any faculty member a question".

Answers are:

So, ∃x[S(x)∧ ∀y{F(y)→ ¬A(x, y)}] OR ∃x[S(x)∧ ¬∃y{F(y)∧A(x, y)}]

Instead, if we bring all the quantifiers at the front, will it cause any difference? Like:

∃x∀y[S(x)∧ {F(y)→ ¬A(x, y)}] OR ∃x¬∃y[S(x)∧ {F(y)∧A(x, y)}]

In general, does it ever cause any change in looping if we bring all quantifiers at the front? Or is there any specific reason not to put all quantifiers at the front?

Thanks

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# I Nested Quantifier Question

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