Please help with this question!!!

Question

Negate the following statement:

                  

Is the negation true or false? Briefly justify your answer.

Answer 1

Fizaa:

The negation of the statement is

(∃x ∈ Z)(∨y ∈ Z) (3x)(y-1) = 0

Or in plain English, there exists an integer x, such that that for all integers y, 3x*(y-1) = 0

Let's think about this statement. If all y are integers, then y-1 is also an integer. So we really need to answer does there exist an integer x such that (3*x) * integer = 0. What about x =0. Does that work? If you need more help, please reach out to me!