Question

Find a counterexample, if possible, to these universally quantified statements, where the domain

for all variables consists of all integers.

a) ∀x (x2 ≥x)

b)∀x(x>0∨x<0) c) ∀x (x = 1)

Answer 1

$a:\\True, \sin ce\,\,x^2-x\geqslant 0 for\,\,x\in \left( -\infty ,0 \right] \left[ 1,+\infty \right) \\which\,\,includes\,\,all\,\,integers\\b:\\x=0-counterexample\\c:\\x=0-counterexample$