Explanation Given Information: The sample space is the set of outcomes of two distinguishable dice when rolled. The subsets E , which has the set of outcomes of at least one die showing an even number, and the set F , which is the set of outcomes in which at least one die is showing an odd number. Consider the provided set with all outcomes of rolling two distinguishable dice to be S . Here the set of outcomes for rolling a dice is from 1 to 6. That is A = { 1 , 2 , 3 , 4 , 5 , 6 } . Since, the dice are distinguishable, thus, the sample space for the toss of two distinguishable dice is, Then, S × S = { 1 , 2 , 3 , 4 , 5 , 6 } = { ( 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 ) } Consider the provided set F which is the set of outcomes in which at least one die shows an odd number. This is represented by, F = { ( 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 ) } Consider the provided set E which is the set of outcomes which at least one die shows an even number

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 6.1, Problem 52E

To determine

The elements in the subset E′∩F′ of the set S which is the set of outcomes of two distinguishable dice when rolled provided that E is the subset of outcomes in which it shows at least one die has an even number and F is the subset of outcomes which has at least one die showing an odd number.

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Chapter 6.1, Problem 51E

Chapter 6.1, Problem 53E

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Finite Mathematics

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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Solution Summary: The author explains that the sample space is the set of outcomes of two distinguishable dice when rolled.

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The elements in the subset E′∩F′ of the set S which is the set of outcomes of two distinguishable dice when rolled provided that E is the subset of outcomes in which it shows at least one die has an even number and F is the subset of outcomes which has at least one die showing an odd number.

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