Example: Check the truth value of these a) $\exists y \in \mathbb{R} \ \forall x \in \mathbb{R} \ (x+y=x)$ b) $\forall x \in \mathbb{R} \ \exists y \in \mathbb{R} \ (x+y=0)$ Example: Check the truth valve of these a) $\forall x \in \mathbb{R} \ \exists y \in \mathbb{R} \ (x+y=x)$ b) $\exists y \in \mathbb{R} \ \forall x \in \mathbb{R} \ (x+y=0)$
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a) $\exists y \in \mathbb{R} \ \forall x \in \mathbb{R} \ (x+y=x)$ This statement says that there exists a real number $y$ such that for all real numbers $x$, $x+y=x$. This is true because if we choose $y=0$, then $x+0=x$ for all $x \in \mathbb{R}$. So the Show more…
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