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. Could you please advise us whether there are any legal implications in the following incidents?

B and C had separately agreed to each sell 50% of their shareholding to D. D is a new investor who wholly owns the 3 major hotels and 3 shopping malls surrounding Hong Kong Studios and whose alliance would form complementary business synergies. In particular, initial discussions and surveys conducted offering "hotel stay and play at theme park and shopping at mall" packages to the public showed that they would be highly popular. However, because D had a falling out with X, Y and Z at last year's Chinese New Year staff banquet because D beat X, Y and Z at the karaoke contest, X, Y and Z refused to register the share transfer saying it was not in the interest of the company that D became a shareholder of Hong Kong Studios. The articles of the company state that "directors may refuse a share transfer if it is in their opinion contrary to the interest of the company that the proposed member becomes a member of the company."

Which directors' duties X, Y and Z have breached and why?