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(Solved): Determine the truth value of each of these statements if the domain of each variable consists of a ...
Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. a) \( \exists x \forall y\left(\left(y=x^{2}\right) \rightarrow x+y>y\right) \) b) \( \forall y \exists x\left(\frac{x}{y}>0\right) \) c) \( \forall x \exists y\left(\left(\sqrt[3]{x} \neq y^{2}\right) \rightarrow(x \geq 0)\right) \) d) \( \exists x \forall y\left(y>0 \rightarrow x^{y} \geq y\right) \)
Expert Answer
a) For this if we choose x>0 then x2=y > 0 i.e., x+y = x+x2 > 0 Now, as x >0 so that x+x2 >x2=y Thus, we get, x>0 such that x+y >y, for all y i