Definition:Matroid/Definition 3

Definition
Let $M = \struct{S,\mathscr I}$ be an independence system.

$M$ is called a matroid on $S$ if $\mathscr I$ also satisfies:

Matroid Axioms
The properties of a matroid are as follows.

For a given matroid $M = \struct{S, \mathscr I}$ these statements hold true: