Please Login to access more options.

Problem 27: (Practice Finding Truth Values With Universal Quantifiers)

Determine the truth value of each statement below. Be prepared to justify your claim.

  1. $\forall x\in \mathbb{R}$ and $\forall y\in \mathbb{R}$, $\exists z\in \mathbb{R}$ such that $x+y=z$.
  2. $\forall x\in \mathbb{R}$ and $\forall y\in \mathbb{R}$, $\exists z\in \mathbb{R}$ such that $xz=y$.
  3. $\forall x\in \mathbb{R}$, $\exists y\in \mathbb{R}$ such that $\forall z\in \mathbb{R}$, $z>y$ implies $z>x+y$.
  4. $\exists x\in \mathbb{R}$ such that $\forall y\in \mathbb{R}$, $\exists z\in \mathbb{R}$ such that $z>y$ implies $z>x+y$.

The following pages link to this page.

Here are the old pages.