Write the negation of each of the following statements Simpl

Write the negation of each of the following statements. Simplify each to the point where no ¬ symbol remains to the left of the expression. Is the statement true? If not, give a counterexample.

Solution

The negation is

there doesn\'t exist a y in R such that for all x in R, x+y=x

Thus, for all y, there exists an x in R such that x+y=/=x

This statement is not true because if we take y=0 then for all x, x+y=x+0=x