Use the following axiomatic system to answer the question:

Axiom 1: There are exactly four Fa's in the system.

Axiom 2: Any two distinct Fa's have exactly one La on both of them.

Axiom 3: Each La is on exactly two Fa's.

a). Give an example of a course model for this geometry and discuss the consistency of the axiomatic system given this model.

b). If two distinct La's intersect, then they have exactly on Fa in common.

c). Determine how many La's must be in the system, and then prove your conjecture. Hint: your model shows the "at least" so you only need to prove there cannot be more.