Answer
a. Statement: For all rational numbers, there exists a pair of integers such that the rational number is the ratio of the two integers.
For all rational numbers r, there exists integers a and b, such that r = a/b.
b. Negation: $\exists r \in \mathbb{Q}$, such that $\forall a, b \in \mathbb{Z}$, r$\neq$a/b.
There exists at least one rational number r such that r is not equal to the ratio of a and b for any integers a and b.
Work Step by Step
Negation of multiply-quantified statement:
~($\forall x$ in D, $\exists y$ in E such that P(x,y)) $\equiv$ $\exists x$ in D such that $\forall y$ in E, ~P(x,y)
