Question #327990

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)

1
Expert's answer
2022-04-14T00:56:08-0400

a:True,sincex2x0forx(,0][1,+)whichincludesallintegersb:x=0counterexamplec:x=0counterexamplea:\\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


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