Anthony loves going to the opera while Becky loves watching football. The following diagram shows the payoffs for their choice of activity. For example, if Anthony chooses opera and Becky chooses football, then the activities are valued at 10 to Anthony and 20 to Becky, respectively. Assume that they can only choose one activity each. Based on this information, determine whether each of the following statements is true or false.

(a) There are two Nash equilibria: (Opera, Opera) and (Football, Football). (b) If Anthony announces that he will choose Opera and sticks to it, then (Opera, Opera) will be chosen. (c) If Anthony offers 20 to Becky for coming to the opera with him, then (Opera, Opera) may be chosen. (d) If Anthony offers 50 to Becky for coming to the opera with him, then (Opera, Opera) will definitely be chosen.