Final answer:
No transactions occurred on July 20 regarding the preference shares. On December 20, 450 preference shares remain from the initial exchange for a building.
Step-by-step explanation:
On July 20, there were no specific transactions mentioned in the question regarding the preference shares. Therefore, it can be assumed that no transactions occurred on that date.
On December 20, 450 preference shares remain from the initial 2,000 preference shares that were exchanged for a building worth $135,000. No further transactions regarding the shares were mentioned in the given information.