Three students are participating in a project. Each of the three students simultaneously chooses whether or not to complete the task assigned to her. The project is successful if and only if all three students complete their tasks. Each student ranks the outcomes from best to worst as follows:

1. Any outcome in which the project is successful and she does not complete her task.

2. Any outcome in which the project is successful and she completes her task.

3. Any outcome in which the project is unsuccessful and she does not complete her task.

4. Any outcome in which the project is unsuccessful and she completes her task. Answer the following questions.

(a) (3 marks) Formulate this situation as a three-player matrix game.

(b) (3 marks) Find all pure strategy Nash equilibria of this game. Show your work.