Suppose we conduct an experiment and S is the set that contains all of its possi

Question

Suppose we conduct an experiment and S is the set that contains all of its possible outcomes. For example, if the experiment is tossing a six-sided dice^1, then S = {1, 2, 3, 4, 5, 6}. If we repeat the experiment k times, the set of outcomes are the elements in the set S^k = S times S times ... times S, the cross product of k copies of S. a. If we toss a dice two times, list all of its possible outcomes. That is, list all the elements in S^2. b. Let A be the set of all elements in S^2 where the first toss produces an even number. Let B consist of all elements in S^2 where the second toss produces an even number. List A B A B A - B B - A B

Explanation / Answer

So there will be 6x6 outcomes = 36 Namely

(1,1) , (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1) , (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1) , (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1) , (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1) , (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1) , (6,2), (6,3), (6,4), (6,5), (6,6).


b) So A = { (2,1) , (2,2), (2,3), (2,4), (2,5), (2,6) , , (4,1) , (4,2), (4,3), (4,4), (4,5), (4,6) ,
(6,1) , (6,2), (6,3), (6,4), (6,5), (6,6). }

B = { (1,2), (1,4), (1,6) , (2,2), (2,4), (2,6), (3,2), (3,4), (3,6), (4,2), (4,4), (4,6), (5,2), (5,4), (5,6), (6,2), (6,4), (6,6) }




AUB = {(1,2), (1,4), (2,1) , (2,2), (2,3), (2,4), (2,5), (2,6) , , (4,1) , (4,2), (4,3), (4,4), (4,5), (4,6) ,
(6,1) , (6,2), (6,3), (6,4), (6,5), (6,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6) }

A Intersection B = { (2,2), (2,4), (2,6) ,(4,2), (4,4), (4,6), (6,2), (6,4), (6,6) }

A - B =. { (2,1) , (2,3), (2,5),, , (4,1) (4,3), (4,5), 6,1) , (6,3), (6,5), }

B-A = { (1,2), (1,4), (1,6) , , (3,2), (3,4), (3,6), (5,2), (5,4), (5,6), }

B complement =. { (1,1) ,(1,3),(1,5), (2,1) , (2,3), , (2,5), (3,1) , , (3,3), (3,5), (4,1) , , (4,3), 4,5),

(5,1) (5,3), (5,5), (6,1) , (6,3), , (6,5), }

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