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 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 ⋃ B and in A ⋂ B? What are the outcomes in Aʹ?