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 ∅ for the empty set.)
(a) list all outcomes in . = 1324,1342,3124,3142,1423,1432,4123, 4132,2314,2341,3214,3241,2413,2431, 4213,4231 (b) let a denote the event that 1 wins the tournament. list outcomes in a. a = {1324,1342,1423,1432} (c) let b denote the event that 2 gets into the championship game. list outcomes in b. b = {2314,2341,3214,3241,2413,2431,4213 ,4231} (d) what are the outcomes in a ∪ b? a ∪ b = {1324,1342,1423,1432,2314,2341,3214 ,3241,2413,2431,4213,4231} what are the outcomes in a ∩ b? a ∩ b = ∅ what are the outcomes in a' ? a' = {3124,3142,1423,4123,4132,2314,2341 ,3214,3241,2413,2431,4213}