Question

If x>7, then |x|>7. |y|>7, so y=7 Valid or invalid?

Answer 1

$\text{if }x>7\text{, then }|x|>7$ is a valid argument

$|y|>7\text{, so }y=7$ is not a valid argument

For the first argument: $\text{if }x>7\text{, then }|x|>7$

From the definition of absolute value function

$|x|=x$   if $x\ge0$

That is every positive number is its own absolute value. Since

$x>7\implies x\ge0$,

we can argue that

$x>7\implies |x|>7$

so the first argument is valid

For the second argument: $|y|>7\text{, so }y=7$

From the definition of absolute value function

$|y|:=\left \{ {y\text{ if }y\ge0}\atop{-y\text{ if }y$

This means that

$|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{-y>7\text{ if }y$

or

$|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{y$

no part of the definition allow for the option $y=7$. So the second argument is not valid.

Learn more here: brainly.com/question/11897796