# I Nested Quantifier Question

1. Apr 10, 2017

### SamitC

Hello,
Suppose a problem statement is :

In a school, suppose S(x) is “x is a student”, F(x) is “x is a faculty member” and A (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".

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:
xy [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

2. Apr 10, 2017

### Staff: Mentor

In this case it doesn't make a difference, but sometimes it can make the expressions harder to read because you have to remember all the variables and their quantifiers before they are actually used.

There could be expressions where it makes a difference, although I don't have an example right now.

3. Apr 10, 2017

Thank you.