Did all mankind fall in Adam's first transgression?

The covenant being made with Adam, not only for himself, but for his posterity; all mankind, descending from him by ordinary generation, sinned in him, and fell with him, in his first transgression.

God created heaven, and earth and sea, and all that is in them. (Acts 4:24) 

God created man in his own image, in the the image of God he created them male and female he created man; for it is through the marriage of a male and female that man is to fill the earth and subdue it, to rule over the fish of the sea, the birds of the sky, and every living thing that moves on the earth. (Gn 1:26-28)

The Lord God placed man in the garden of Eden to cultivate it and keep it. He told man that he could eat freely from any tree in the garden except from the tree of the knowledge of good and evil. God warned man that doing so would result in death. (Gn 2:15-17)

The man and the woman both ate from the tree of the knowledge of good and evil; (Gn 3:16) therefore, all of mankind became condemned because of the sin of our first parents. (Rom 5:18)