Respuesta :

[tex]\text{if }x>7\text{, then }|x|>7[/tex] is a valid argument

[tex]|y|>7\text{, so }y=7[/tex] is not a valid argument

For the first argument: [tex]\text{if }x>7\text{, then }|x|>7[/tex]

From the definition of absolute value function

[tex]|x|=x[/tex]   if [tex]x\ge0[/tex]

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

[tex]x>7\implies x\ge0[/tex],

we can argue that

[tex]x>7\implies |x|>7[/tex]

so the first argument is valid

For the second argument: [tex]|y|>7\text{, so }y=7[/tex]

From the definition of absolute value function

[tex]|y|:=\left \{ {y\text{ if }y\ge0}\atop{-y\text{ if }y<0} }\right[/tex]

This means that

[tex]|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{-y>7\text{ if }y<0} }\right[/tex]

or

[tex]|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{y<-7\text{ if }y<0} }\right[/tex]

no part of the definition allow for the option [tex]y=7[/tex]. So the second argument is not valid.

Learn more here: https://brainly.com/question/11897796