This problem is based on the Gale-Shapley Algorithm.

In each iteration of the while loop, choose an arbitrary unmatched teacher j. Next, j makes an offer to the highest teacher on thier list whom j has not yet made an offer to yet.

Statement: If some teacher j makes an offer to j0 and they match forming (j, j0 ), then j will reject any future offers while still matched to j0

Proof. This is true because j has already previously made offers to every teacher they prefer over j0 . (This is false)

Briefly explain why the above Statement is false by explaining a circumstance that would lead to j accepting another proposal while matched to j0.