2. Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the integer (a-b) is divisible by 4. List the elements of R and its inverse? b) Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where R = {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the following properties R has: reflexive, symmetric, anti-symmetric, transitive? Justify your answer in each case? Let S = {a, b, c} and R = {(a, a), (b, b), (c,c), (b,c), (c,b)}, find [a], [b] and [c] (that is the equivalent class of a, b, and c). Hence or otherwise find the c) set of equivalent class of a, b and c?

2. Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the integer (a-b) is divisible by 4. List the elements of R and its inverse? b) Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where R = {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the following properties R has: reflexive, symmetric, anti-symmetric, transitive? Justify your answer in each case? Let S = {a, b, c} and R = {(a, a), (b, b), (c,c), (b,c), (c,b)}, find [a], [b] and [c] (that is the equivalent class of a, b, and c). Hence or otherwise find the c) set of equivalent class of a, b and c?

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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Similar questions

6. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation xRy when x + y is divisible by 3, then R = O {1, 2), (2, 4)} all of these O {(1, 2), (2, 4), (3, 3)} O {1, 2), (3, 3)}
Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and not transitive.
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Let ? = {1, 2, 3, 4, 5, 6, 7} and define a relation ? ⊆ ? × ? by? = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}Determine (yes or no) whether ? has the following properties (no justification is required).
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Let X=\{a,b,c,d,e,f\}X={a,b,c,d,e,f} and SS be the relation on XX defined by S = \{ (a,a), (a,b), (a,c),S={(a,a),(a,b),(a,c), (a,d), (a,e), (a,f),(a,d),(a,e),(a,f), (b,b), (b,d), (b,e),(b,b),(b,d),(b,e), (b,f), (c,c), (c,d),(b,f),(c,c),(c,d), (c,e), (c,f), (d,d),(c,e),(c,f),(d,d), (d,e), (d,f), (e,e), (f,f) \}(d,e),(d,f),(e,e),(f,f)}. Is SS a partial order? If so, draw its Hasse diagram. If not, give an example showing why.