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}

i.   A∪B = (1324,1342,1423,1432,2314,2341,3214,3241,2413,1431,4213,4231)

ii.    A¹ = (3124,3142,4123,4132,2314,2341,3214,3241,2413,2431,4213,4231)

Step-by-step explanation:

A union set is the collection of elements in two or more subsets. Here set A is equal to (1324,1342,1423,1432) and set B is equal to (2314,2341,3214,3241,4213,4231,3214,3241).

A∪B = (1324,1342,1423,1432,2314,2341,3214,3241,2413,1431,4213,4231)

ii. the complement of a set represent those elements in the universal set which are not in a given subset.

U = (1324,1342,3124,3142,1423,1432,4123,4132,2314,2341,3214,3241,2413,2431,4213,4231),

 A¹ =  (3124,3142,4123,4132,2314,2341,3214,3241,2413,2431,4213,4231).this represents elements in the universal set U which are not in the set of A.

step-by-step explanation:

i believe its "c" because all of the other options include a but it could be d because there is a way of financing with cash at certain places but its uncommon.

on a coordinate grid, point a is at (−4.0, −2.4) and point b is at (4.0, −2.4). point b is a reflection of point a across the –axis. input either a lowercase x or i think is the right awnser

step-by-step explanation: