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Let X = {a, b, c), and let P(X) be the power set of X. Define a relation N on P(X) as follows. For every A, BE P(X), ANB the number of elements in A is not equal to the number of elements in B. (a) Is N reflexive? --Select--- V, N is reflexive for every set A in P(X), A NA. By definition of N this means that for every set A in P(X), the number of elements in A ---Select--- (b) Is N symmetric? ✓ the number of elements in A. This is ---Select--- ✓ for every set in P(X). Thus, N ---Select--- reflexive. --Select--- ✓ because for all sets A and B in P(X), if the number of elements in A --Select--- the number of elements in B, then the number of elements in B --Select--- the number of elements in A. (c) Is N transitive? N is transitive if, and only if, for all sets A, B, and C in P(X), if the number of elements in A ---Select--- the number of elements in B and the number of elements in B C. One or more of the following examples can be used to show that N ---Select--- ✓ transitive according to this definition. (Select all that apply.) -Select--- the number of elements in C, then the number of elements in A -Select--- ✓ the number of elements in A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5} ☐ A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5, 6, 7} A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, C = {3, 4, 5}

Let X = {a, b, c), and let P(X) be the power set of X. Define a relation N on P(X) as follows. For every A, BE P(X), ANB the number of elements in A is not equal to the number of elements in B. (a) Is N reflexive? --Select--- V, N is reflexive for every set A in P(X), A NA. By definition of N this means that for every set A in P(X), the number of elements in A ---Select--- (b) Is N symmetric? ✓ the number of elements in A. This is ---Select--- ✓ for every set in P(X). Thus, N ---Select--- reflexive. --Select--- ✓ because for all sets A and B in P(X), if the number of elements in A --Select--- the number of elements in B, then the number of elements in B --Select--- the number of elements in A. (c) Is N transitive? N is transitive if, and only if, for all sets A, B, and C in P(X), if the number of elements in A ---Select--- the number of elements in B and the number of elements in B C. One or more of the following examples can be used to show that N ---Select--- ✓ transitive according to this definition. (Select all that apply.) -Select--- the number of elements in C, then the number of elements in A -Select--- ✓ the number of elements in A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5} ☐ A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5, 6, 7} A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, C = {3, 4, 5}

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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Let X = {a, b, c), and let P(X) be the power set of X. Define a relation N on P(X) as follows. For every A, BE P(X), ANB the number of elements in A is not equal to the number of elements in B. (a) Is N reflexive? --Select--- V, N is reflexive for every set A in P(X), A NA. By definition of N this means that for every set A in P(X), the number of elements in A ---Select--- (b) Is N symmetric? ✓ the number of elements in A. This is ---Select--- ✓ for every set in P(X). Thus, N ---Select--- reflexive. --Select--- ✓ because for all sets A and B in P(X), if the number of elements in A --Select--- the number of elements in B, then the number of elements in B --Select--- the number of elements in A. (c) Is N transitive? N is transitive if, and only if, for all sets A, B, and C in P(X), if the number of elements in A ---Select--- the number of elements in B and the number of elements in B C. One or more of the following examples can be used to show that N ---Select--- ✓ transitive according to this definition. (Select all that apply.) -Select--- the number of elements in C, then the number of elements in A -Select--- ✓ the number of elements in A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5} ☐ A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5, 6, 7} A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, C = {3, 4, 5}
Transcribed Image Text:Let X = {a, b, c), and let P(X) be the power set of X. Define a relation N on P(X) as follows. For every A, BE P(X), ANB the number of elements in A is not equal to the number of elements in B. (a) Is N reflexive? --Select--- V, N is reflexive for every set A in P(X), A NA. By definition of N this means that for every set A in P(X), the number of elements in A ---Select--- (b) Is N symmetric? ✓ the number of elements in A. This is ---Select--- ✓ for every set in P(X). Thus, N ---Select--- reflexive. --Select--- ✓ because for all sets A and B in P(X), if the number of elements in A --Select--- the number of elements in B, then the number of elements in B --Select--- the number of elements in A. (c) Is N transitive? N is transitive if, and only if, for all sets A, B, and C in P(X), if the number of elements in A ---Select--- the number of elements in B and the number of elements in B C. One or more of the following examples can be used to show that N ---Select--- ✓ transitive according to this definition. (Select all that apply.) -Select--- the number of elements in C, then the number of elements in A -Select--- ✓ the number of elements in A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5} ☐ A = {1, 2, 3, 4, 5}, B = {3, 4, 5}, C = {3, 4, 5, 6, 7} A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, C = {3, 4, 5}
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