Question

What is nested Quantifier? Is order important for nested quantifier?

Explain your answer with appropriate example.

Answer 1

nested Quantifier :

Nested quantifiers are quantifiers that occur within the scope of other quantifiers.

Example: $∀x∃yP(x,y)$

The order of nested existential and universal quantifiers in a statement is important.

Quantification of two variables

$∀x∀yP(x,y)$

P(x,y) is true for every pair x,y.

There is a pair x, y for which P(x,y) is false.

$∀x∃yP(x,y)$

For every x there is a y for which P(x,y) is true.

There is an x such that P(x,y) is false for every y.