Answer
a. Version with interchanged quantifiers: ∃x ∈ R such that ∀y ∈ R, x < y.
b. The given statement is true. The statement with exchanged quantifiers (part a) is false.
Work Step by Step
b. The given statement says that for any real number x, there is a real number y that is greater than x. This is true: For any real number x, let y = x + 1. Then x < y.
The version with interchanged quantifiers says that there is a real number that is less than every other real number. This is false.
