Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.2 - Page 116: 5

a. There exists a valid argument that has false conclusion. b. There exists a real number that is not positive, not negative, and not zero.

Negation of the statements of the form, "For all x, q", q being a statement, is "There exists x, ~q". Negation of the statements of the form, "There exists x, ~q", q being a statement, is "For all x, q".