Let M be a free R-module where R is commutative ring with unity.
Q1: If M is FG by n vectors. Will rankM $\leq$ n?
Q2: If M has a LI set $S$. Will #$S \leq$ rankM?
What if R is PID?
Are above results true for FG free abelian groups which are free module over Z?
What will be answers in case FG by n vectors, replaced by generated by a set of infinite cardianlity and Q2 also looked for free modules of infinite cardianlity?