The presentation of a group I am confused with the following definitions from Dummit &amp; Foote

"In general, if some group $G$ is generated by a subset $S$ and there is some collection of relations, say $R_1,\ldots, R_m$(here each $R_i$ is an equation in the elements from $S \cup \{1\}$ such that any relation among the elements of $S$ can be deduced from these, we shall call these generators a presentation of $G$"

I have two questions:

1.Shouldn't the relation come from $S \cup \{1\} \cup$ all the inverses of $S$ rather than only from $S \cup \{1\}$.

2.What does it mean by saying that one relation can be deduced from a set of relations.
Yes
Given an arbitrary relation $R$ in $G$, $R_1,\dots, R_m$ imply $R$
Yes
Given an arbitrary relation $R$ in $G$, $R_1,\dots, R_m$ imply $R$