Answer
a. Statement: there exists a real number x such that for all real numbers y, x+y=0.
There is a real number that when that real number is added to any real number, the sum is zero.
b. $\forall x \in \mathbb{R}$, $\exists y \in \mathbb{R}$ such that x+y$\neq$0.
For every real number, there is another real number such that the sum of the two numbers is nonzero.
For every real number x, there is a real number y, such that x+y$\neq$0.
Work Step by Step
Negation of a multiply-quantified statement:
~($\exists x$ in D such that $\forall y$ in E, P(x,y)) $\equiv$ $\forall x$ in D, $\exists y$ in E such that ~P(x,y)
