Answer
a. Statement: For every real number x, there is a real number y such that x + y = 0.
Given any real number x, there exists a real number y such that x + y = 0.
Given any real number, we can find another real number (possibly the same) such that the sum of the given number plus the other number equals 0.
Every real number can be added to some other real number (possibly itself) to obtain 0.
b. Negation: ∃ a real number x such that ∀ real numbers y, x + y $\neq$ 0.
There is a real number x for which there is no real number y with x + y $\neq$ 0.
There is a real number x with the property that x + y $\neq$ 0 for any real number y.
Some real number has the property that its sum with any other real number is nonzero.
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)
