חוה - Eve

In the Book of Genesis there is a very subtle detail that teaches an important principle about the fall. This detail has to do with the introduction of Eve in the Biblical account of Adam and Eve. The name Eve comes from the Hebrew חוה (Hava) which means "lifegiver" according to Strong's Hebrew and Greek Dictionary, or "mother of all living" according to the Bible (see Genesis 3:20).

We know from the Book of Mormon that had Adam and Eve not partaken of the fruit of the tree of knowledge of good and evil they would have remained in the garden in a state of innocence without the ability to procreate. See 2 Nephi 2:22-23. In the book of Genesis the name Eve doesn't appear until Genesis 3:20 and she is referred to as "the woman" prior to that. Probably Eve was referred to as "the woman" prior to the fall because she wasn't a candidate for motherhood until after she and Adam partook of the fruit. Once she partook of the fruit the woman could rightly be called "Eve".

Moses chapter 5

10 And in that day Adam blessed God and was filled, and began to prophesy concerning all the families of the earth, saying: Blessed be the name of God, for because of my transgression my eyes are opened, and in this life I shall have joy, and again in the flesh I shall see God.

11 And Eve, his wife, heard all these things and was glad, saying: Were it not for our transgression we never should have had seed, and never should have known good and evil, and the joy of our redemption, and the eternal life which God giveth unto all the obedient.

12 And Adam and Eve blessed the name of God, and they made all things known unto their sons and their daughters.