Let the universe for the variables in the following statements consist of all real numbers. In each case negate and simplify the given statement.
a) ∀x ∀y [(x < y) → (x– y < 0)]
b) ∀x ∀y [(x<y) → ∃z (x<z < y)]
c) ∀x ∀y [(|x| = |y|) → (y = ±.x)]
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