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). (Enter your answers in set notation. Enter EMPTY or $\emptyset$ for the empty set.)
(a) List all outcomes in $S$.
$S=$
(b) Let $A$ denote the event that 1 wins the tournament. List outcomes in $A$.
$A=$
(c) Let $B$ denote the event that 2 gets into the championship game. List outcomes in $B$.
$B=$
(d) What are the outcomes in $A \cup B$?
$A \cup B=$
What are the outcomes in $A \cap B$?
$A \cap B=$
What are the outcomes in $A'$?
$A'=$
