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4. Given s and t, relations on Z, s = {(1,n) : n € Z} and t = {{n,1) : n E Z}, what are st and ts? Hint: Even when a relation involves infinite sets, you can often get insights into them by dråwing partial graphs.

4. Given s and t, relations on Z, s = {(1,n) : n € Z} and t = {{n,1) : n E Z}, what are st and ts? Hint: Even when a relation involves infinite sets, you can often get insights into them by dråwing partial graphs.

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 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...
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4, 5} ahd défine r on A by cry iff x + 1=y. We define p2 and =r. Find: b. p2 Answer 4. Given s and t, relations on Z, s = {(1,n) : n E Z} and t = {(n, 1) : n E Z}, what are st and ts? Hint: Even when a relation involves infinite sets, you can often get insights into them by dråwing partial graphs. 5. Let p be the relation on the power set, P(S), of a finite set S of cardinality defined p by (A, B) e p iff An B = 0. Consider the specific case n = 3, and determine the cardinality of the s a. p. b. What is the cardinality of p for an arbitrary n? Express your answer in terms of n. (Hint: There are three places that each element of S can go
Transcribed Image Text:4, 5} ahd défine r on A by cry iff x + 1=y. We define p2 and =r. Find: b. p2 Answer 4. Given s and t, relations on Z, s = {(1,n) : n E Z} and t = {(n, 1) : n E Z}, what are st and ts? Hint: Even when a relation involves infinite sets, you can often get insights into them by dråwing partial graphs. 5. Let p be the relation on the power set, P(S), of a finite set S of cardinality defined p by (A, B) e p iff An B = 0. Consider the specific case n = 3, and determine the cardinality of the s a. p. b. What is the cardinality of p for an arbitrary n? Express your answer in terms of n. (Hint: There are three places that each element of S can go
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