Answer
a. Version with interchanged quantifiers: $\forall x \in \mathbb{R}$, $\exists y \in \mathbb{R}^{-}$ such that x > y.
b. Both the original and the interchanged statement are true.
Work Step by Step
b. The original statement says there is a real number that is greater than every negative real number. This is true. Let that real number x be 0 which is greater than every negative real number.
The statement with interchanged quantifiers says for every real number x, there is a negative real number y that is less than x. This is true. Let y = -|x| - 1. Then x>y for all x.
