Question
Translate these statements into English, where the domain for each variable consists of all real numbersa) $\exists x \forall y(x y=y)$b) $\forall x \forall y(((x \geq 0) \wedge(y<0)) \rightarrow(x-y>0))$c) $\forall x \forall y \exists z(x=y+z)$.
Step 1
The symbol $\exists$ means "there exists", $\forall$ means "for all", and $\rightarrow$ means "implies". Show more…
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Translate these statements into English, where the domain for each variable consists of all real numbers a) $\exists x \forall y(x y=y)$ b) $\forall x \forall y(((x \geq 0) \wedge(y<0)) \rightarrow(x-y>0))$ c) $\forall x \forall y \exists z(x=y+z)$.
Translate these statements into English, where the domain for each variable consists of all real numbers. a) $\quad \forall x \exists y(x<y)$ b) $\forall x \forall y(((x \geq 0) \wedge(y \geq 0)) \rightarrow(x y \geq 0))$ c) $\forall x \forall y \exists z(x y=z)$
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Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. a) $\exists x \forall y(x y=y)$ b) $\forall x \forall y(((x<0) \wedge(y<0)) \rightarrow(x y>0))$ c) $\exists x \exists y\left(\left(x^{2}>y\right) \wedge(x<y)\right)$ d) $\forall x \forall y \exists z(x+y=z)$
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