Question

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}

Answer 1

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)

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.