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Decide truth values of the following statements, assuming x,y,z are real numbers. Justify your answers. Then write the negation of each statement.

a).  \forall x \exists y, x+y=0

b).  \forall x \forall y \exists z, x=yz

Now for a). I used the logic that if we are given any x, let y= 0-x thus any x can be used to solve for a y. However for the second statement I am not sure how to go about it, as I had the same idea to say let x and y be any real number, then z = x/y however if x and y = 0 then this is not a true statement as 0/0 is undetermined. Not sure if this is correct or if I am missing something, please help.

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