X, Y and Z are professional accountants by training and were appointed for their professional accounting skills, business acumen and dedication to the company. However, X, Y and Z have proven to be very disappointing. Several incidents have occurred recently that have caused us some concerns.

1.X, Y and Z used their powers to acquire 2 bank loans for the company to purchase a small, independent but failing Hong Kong broadcasting company that X holds a majority shareholding in and has not disclosed to the board. When X, Y and Z held the board meeting to pass the resolution to obtain the bank loans on behalf of the company to buy the small failing broadcasting company, Y and Z did not question the proposal when X said at the board meeting that "he thought was a good idea."

Which directors' duties X, Y and Z have breached and give reasons for your answer. (In your answer consider whether X (as director) can use his powers to acquire loans on behalf of "Hong Kong Studios" to purchase his failing company? And what is the fault of Y and Z?)