Question

Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. [These pairs can be listed, for example, by letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second.] a Define the following subsets of S: A: The number on the second die is even. B: The sum of the two numbers is even. C: At least one number in the pair is odd. b Listthepointsin A,C,A∩B,A∩B,A∪B,and A∩C.

Answer 1

Answer:

The set A={(1,2),(2,2),(3,2),(4,2),(5,2),(6,2),(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(1,(2,6),(3,6),(4,6),(5,6),(6,6)}

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

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

A∩B:{(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6)}

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

A∩C={(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

Step-by-step explanation:

Answer 2

Answer: SubsetA:the second number on the dice is even

(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)

SubsetB

That the sum of the two number is even

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

SubsetC:at least one number is odd

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

(2,1),(2,3),(2,5)

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

(4,1),(4,3)(4,5)

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

AnB

(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2)(6,4),(6,6)

AUB

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

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

(4,2),(4,4),4,6

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

6,2),(6,4),(6,6)

AnC

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

Step-by-step explanation:

We use the decision table,the row representing the numbers. On the surface of the first dice

While the column represent the second dice

Number inside represent the possible addition of the two dices when thrown.

123456

1 23456

2345678

3456789

45678910

567891011

67891011112