Solution for Section 2.2 Question 3

3. Recall that the negation of  $ x such that " y, P(x,y)   is " x, $ y such that ~P(x,y).

The negation of this statement is " x R, $ y R such that  xy 0.

The original statement is true since there does exist a real number (x = 0) such that for every real number y, xy = 0.
The negation is false since it does not hold when x = 0.

Back to Section 2.2