Example of properties so that "any two properties imply the third"

(Not nonmathematical)

In an $n$-dimensional vector space consider the statements about a subset $S$:

• $S$ is independent.
• $S$ spans.
• $S$ has cardinality $n$.

1. One dollar is worth $\frac67$ euro.
2. One euro is worth $\frac78$ pounds.
3. One pound is worth $\frac43$ dollars.