Question

negate the statement below

Answer 1

hu?

Answer 2

\[(\forall y \in \mathbb{R}) [y>0 \implies (\exists x \in \mathbb{R} s.t. (y=e^x)]\]

Answer 3

Recall that:\[\Large\rm P\implies Q \qquad\equiv\qquad \neg P \wedge Q\]

Answer 4

So let's see....

Answer 5

\[\Large\rm \forall y \in \mathbb{R}, \qquad y>0 \implies (\exists x \in \mathbb{R}:y=e^x)\]So we want to negate this.. ummm
So we'll write it as:\[\Large\rm \forall y \in \mathbb{R}, \qquad y\le0 ~or~ (\exists x \in \mathbb{R}:y=e^x)\]It should be a little easier to negate from here, yes?

Answer 6

I changed the interval for y, (changed it to NOT p)

Answer 7

\[\Large\rm \exists y\in \mathbb R:\qquad y\gt0~and~(\forall x\in\mathbb R,\quad y\ne e^x)\]Something like that I think.
Yah?

Answer 8

i think so, thank you!

Answer 9

np c: