Please Login to access more options.

Problem 40: (Practice Finding Truth Values With Universal Quantifiers 2)

For each statement below, first write the negation. Then determine whether the statement or the negation is true, and justify your claim. In your work below, assume that $f(x)=x^2$.

  1. $\forall x\in \mathbb{R}$, $\exists y\in \mathbb{R}$ such that $\forall z\in \mathbb{R}$ we have $x+y=z$.
  2. $\forall x,y\in \mathbb{R}$, $\exists z\in \mathbb{R}$ such that $x+z=y$.
  3. $\exists x\in \mathbb{R}$ such that $\forall y\in \mathbb{Z}$, $x<y$ implies $f(x)<f(y)$.
  4. $\forall x,y\in \mathbb{R}$, if $f(x)=f(y)$ then $x=y$.

The following pages link to this page.

Here are the old pages.