jeffro -In the version I have, God doesn’t tell Eve (who doesn’t get a name until later in the story) anything about either tree, and only tells Adam about the tree of knowledge. The story doesn’t state whether Eve is directly told by God about the tree of knowledge or whether it’s via Adam, but it doesn’t say either are told about the tree of life.
Here is Genesis chapter 2
15 "The Lord God took the man and put him in the Garden of Eden to work it and take care of it. 16 And the Lord God commanded the man, “You are free to eat from any tree in the garden; 17 but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die"
God prohibited Adam and Eve to eat from only ONE tree. They could eat from all the other trees to their hearts content. This included the tree of life.
As presented in the story, the snake didn’t lie when it said that eating the knowledge fruit doesn’t itself cause death.
God said of the wrong tree, and Eve repeated in the next chapter, "for when you eat from it you will certainly die".
The snake said the exact opposite thing as the words above..."you will not certainly die".