Four universities -- 1,2,3 and 4 -- are participating in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play for the championship, and the two losers will also play. One possible outcome can be denoted by 1324 (1 beats 2 and 3 beats 4 in first round games, and then 1 beats 3 and 2 beats 4).

A. List all outcomes in $\mathcal{S}$.
B. Let $A$ denote the event that 1 wins the tournament. List outcomes in $A$.
C. Let $B$ denote the event that 2 gets into the championship game. List outcomes in $B$.
D. What are the outcomes in $A\cup B$ and in $A\cap B$? What are the outcomes in $A^{c}$?
 

Reference:

Jay L. Devore, Probability and Statistics, For Engineering and The Sciences (Fifth Edtion)