Consider an infinite set of undefined elements S and the undefinedrelation R that satisfies the following axioms:Axiom 1. If a, b e S and a Rb, then a #b.Axiom 2. If a, b, c e S, a Rb, and bRc, then a Rc.(i) Show that an interpretation with S as the set of integers anda Rb as "a is less than b" is a model for the system.(ii)Would S as the set of integers and a Rb interpreted as "a isgreater than b" also be a model?(iii) Are the models in parts (a) and (b) isomorphic?(iv) Would S as the set of real numbers and a Rb interpreted as"a is less than b" be another model?(v) Is the model in part (d) isomorphic to the model in part (a)?

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Answered: Consider an infinite set of undefined…

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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6. Q6; Relations (a) Define relations S and R on the set A = {a, b, c, d} as follows: {(a, b), (b, c), (c, d), (b, b)}, S = R = {(b, a), (c, c), (a, c), (d, b)}. i. Find So S, So R, R-o So R. Is R-lo SoR= S ? ii. Determine which of S, R, So R, S-1 or R-1 is a function. (b) Let R = {(x, y) E R × R : 1
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15 Part 2 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R6 = {(a, b) ER² | a b), the unequal to relation For these relations on the set of real numbers, find R₁⁰ R₁. Multiple Choice O O R₁ O R4
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A4. a. Draw a Digraph represented by the adjacency matrix 1 1 1 1 1 1 1 b. Consider the recurrent relationA, = 2An-1 + 3An-2, where n 2 2 and A = 1, A, = 2. Compute the next 4 terms (A2, A3, A4, A5) of the relation.

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