2.Suppose A = {1, 2, 3, 4, · .. , 14, 15} and let R be the relation of congruence modulo5 on the set A denoted byI = y (mod 5) .This mean that the difference xy is divisible by 5.(a) Show that R is an equivalence relation on A.(b) Find the quotient set A/R.

Answered: Image /qna-images/answer/5c6e7b17-9e1e-4bb2-a457-c4e277dc39a7.jpg

Answered: 2. Suppose A = {1, 2, 3, 4, .. , 14,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 2 List all possible equivalence relations on the set {1,2,3,4} without repetition up to isomorphism. Justify your answer.
) 7. Let A = {1,2,3,4}×{1,2,3,4}. Define an equivalence relation - by (x1,x2) ~ (X3,x4) iff x1x2 = xx4. List the elements of the equivalence class [(2,2)].
From the options below, select the ones which are true for the relation ~ on the set of real numbers that is defined by x ~ y if x ≤y. is an equivalence relation O~ is reflexive ~ is transitive O ~ is symmetric ONone of the above
5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a
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Let R be the relation on the set of all mathematicians that contains the ordered pair (a, b) if and only if a and b have written a published mathematical paper together. a) Describe the relation R[2] in the context of the problem.b) Describe the relation R* in the context of the problem.c) The Erdos number of a mathematician is 1 if this mathematician wrote a paper with the prolific Hungarian mathematician Paul Erdos. The Erdos number is 2 if a mathematician didn’t write a joint paper with Erdos but wrote a joint paper with someone who wrote a joint paper with Erdos, and so on (except that the Erdos number of Erdos himself is 0). Give a definition of the Erdos number is terms of paths in R. List a name of a mathematician with number: 1, 2, and 3
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2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set A denoted by I = y (mod 5) . This mean that the difference x - y is divisible by 5. (a) Show that R is an equivalence relation on A. (b) Find the quotient set A/R.