Answer to Question #132566 in Discrete Mathematics for Promise Omiponle

Question

(5) Find a counterexample, if possible, to these universally quantified statements, where
the domain for all variables consists of all integers.
(a)∀x∃y(x= 1/y)
(b)∀x∃y(y^2-x <100)
(c)∀x∀y(x^2=/=y^3)

Answer 1

a) $x=2, y=1, x\ne1/1$

b) $x=1, y=20, 20^2-1>100$

c) $x=8, y=4, 8^2=4^3$