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Assume that R and S are symmetric relations on a set A. Is R n S symmetric? Fill in the blanks to answer this question. Suppose x and y are any elements of A such that (x, y) is in R n S. Since (x, y) ER n S, then (x, y) ER ---Select--- ✓ ---Select--- ✓ by definition of ---Select--- ✓ Now ---Select-- ✓ because R is ---Select--- and ---Select--- Thus, ---Select--- E ---Select--- ✓ by definition of ---Select--- ✓ because S is ---Select--- Since x and y could be any elements of A, this shows that for ---Select--- Hence, R n S ---Select--- ✓ symmetric. elements x and y in A, if (x, y) ER n S, then ---Select--- ? |---Select--- ✓

Assume that R and S are symmetric relations on a set A. Is R n S symmetric? Fill in the blanks to answer this question. Suppose x and y are any elements of A such that (x, y) is in R n S. Since (x, y) ER n S, then (x, y) ER ---Select--- ✓ ---Select--- ✓ by definition of ---Select--- ✓ Now ---Select-- ✓ because R is ---Select--- and ---Select--- Thus, ---Select--- E ---Select--- ✓ by definition of ---Select--- ✓ because S is ---Select--- Since x and y could be any elements of A, this shows that for ---Select--- Hence, R n S ---Select--- ✓ symmetric. elements x and y in A, if (x, y) ER n S, then ---Select--- ? |---Select--- ✓

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 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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Assume that R and S are symmetric relations on a set A. Is R n S symmetric? Fill in the blanks to answer this question. Suppose x and y are any elements of A such that (x, y) is in R n S. Since (x, y) ER n S, then (x, y) ER ---Select--- ✓ ---Select--- ✓ by definition of ---Select--- ✓ Now ---Select-- ✓ because R is ---Select--- and ---Select--- Thus, ---Select--- E ---Select--- ✓ by definition of ---Select--- ✓ because S is ---Select--- Since x and y could be any elements of A, this shows that for ---Select--- Hence, R n S ---Select--- ✓ symmetric. elements x and y in A, if (x, y) ER n S, then ---Select--- ? |---Select--- ✓
Transcribed Image Text:Assume that R and S are symmetric relations on a set A. Is R n S symmetric? Fill in the blanks to answer this question. Suppose x and y are any elements of A such that (x, y) is in R n S. Since (x, y) ER n S, then (x, y) ER ---Select--- ✓ ---Select--- ✓ by definition of ---Select--- ✓ Now ---Select-- ✓ because R is ---Select--- and ---Select--- Thus, ---Select--- E ---Select--- ✓ by definition of ---Select--- ✓ because S is ---Select--- Since x and y could be any elements of A, this shows that for ---Select--- Hence, R n S ---Select--- ✓ symmetric. elements x and y in A, if (x, y) ER n S, then ---Select--- ? |---Select--- ✓
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