4. a)Define the following terms:i)POSETSii)Equivalence relationb)Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on Aas follows:For every (x, y) eA,xRy + 5 divides (x² – y²) and

Name: 4. a)Define the following terms:i)POSETSii)Equivalence relationb)Let
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Description: 4. a)Define the following terms:i)POSETSii)Equivalence relationb)Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on Aas follows:For every (x, y) eA,xRy + 5 divides (x² – y²) and

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Answered: a) Define the following terms: i)…

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Advanced Math

a) Define the following terms: i) POSETS ii) Equivalence relation

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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b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W, X, Y and Z. We define the relation: A Sesotho word x is related to another Sesotho word y if x begins with the same letter as y. Determine whether or not this is an equivalence relation. If it is an equivalence relation then 1. Compute C(sekatana) 2. How many equivalence classes are there in all, and why? 3. What is the partition of the English words under this relation? If it is NOT an equivalence relation then explain in details why it is not.
3. Use our known logical equivalence rules to show the following equivalence: - (pA (gV p)) = ~ pV ~q
please send handwritten solution for part b
A) List all reflexive relations can be defined on set {a, b}. B) List all ordered pairs in the partial ordering for the following Hasse diagram: C) Is the above a total ordering?
b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W, X, Y and Z. We define the relation: A Sesotho word x is related to another Sesotho word y if x begins with the same letter as y. Determine whether or not this is an equivalence relation. If it is an equivalence relation then 1. Compute C(sekatana) 2. How many equivalence classes are there in all, and why? 3. What is the partition of the English words under this relation? If it is NOT an equivalence relation then explain in details why it is not.
Suppose A and B are two finite sets such that |B| = |A| - 1 and the number of relations on A is 512. Determine: |B|: Number of relations from B to A: