Find a counterexample, if possible, to these universally

QUESTION:

Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers.

a) \(\forall x \forall y\left(x^{2}=y^{2} \rightarrow x=y\right)\)

b) \(\forall x \exists y\left(y^{2}=x\right)\)

c) \(\forall x \forall y(x y \geq x)\)

Equation Transcription:

∀x∀y(x2 = y2 → x = y)

∀x∃y(y2 = x)

∀x∀y(xy ≥ x)

Text Transcription:

forall x \forall y\left(x^{2}=y^{2} \rightarrow x=y\right)

forall x \exists y\left(y^{2}=x\right)

forall x \forall y(x y \geq x)