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4. Find the equivalence classes for each of the following equivalence relations R on the given...
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given...
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given set A, determine whether or not it is reflexive, symmetric, anti-symmetric, or transitive. Explain why. (a) A = {0, 1,2,3), R = {(0,0).(0,1),(1,1),(1,2).(2, 2), (2.3)} (b) A = {0, 1,2,3), R = {(0,0).(0,2), (1,1),(1,3), (2,0), (2,2), (3,1),(3,3)} (c) A is the set of all English words. For words a and b, (a,b) E R if and only if a and b have at least...
Consider the following binary relations R1, R2, and R3 below, each defined over the set of...
Consider the following binary relations R1, R2, and R3 below, each defined over the set of integers between 0 and 4 inclusive and with each tuple (a,b) indicating that a is related to b. R1 = {(0,0), (0,3), (1, 1), (1, 2), (2,0), (2,3), (3, 1), (3,4), (4,0), (4,1)} R2 = {(1, 2), (2, 2), (3,0), (3,2), (4,0), (4,3)} R3 = {(0,0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} Which of these three relations is an...
1. (14 points) (a) For each of the following relations R on the given domains A,...
1. (14 points) (a) For each of the following relations R on the given domains A, categorize them as not an equivalence relation, an equivalence relation with finitely many distinct equivalence classes, or an equivalence relation with infinitely many distinct equivalence classes. Justify each decision with a brief proof. (i) A = {1, 2, 3} , R = {(1, 1),(2, 2),(3, 3)} (ii) A = R, R = {(x, y) | x 2 = y 2} (iii) A = Z,...
ANSWER 2 & 3 please. Show work for my understanding and upvote. THANK YOU!! 2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip...
ANSWER 2 & 3 please. Show work for my understanding and
upvote. THANK YOU!!
2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip over the n-gon. These n actions form a group denotecd (a) Draw a Cayley diagram for Cn for n-4, n-5, and n-6 (b) For n 4, 5, 6, find all minimal generating sets of C.· [Note: There are minimal generating sets...
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given set A, determine whether or not it is reflexive, symmetric, anti-symmetric, or transitive. Explain why. (a) A = {0, 1,2,3), R = {(0,0).(0,1),(1,1),(1,2).(2, 2), (2.3)} (b) A = {0, 1,2,3), R = {(0,0).(0,2), (1,1),(1,3), (2,0), (2,2), (3,1),(3,3)} (c) A is the set of all English words. For words a and b, (a,b) E R if and only if a and b have at least...
Consider the following binary relations R1, R2, and R3 below, each defined over the set of integers between 0 and 4 inclusive and with each tuple (a,b) indicating that a is related to b. R1 = {(0,0), (0,3), (1, 1), (1, 2), (2,0), (2,3), (3, 1), (3,4), (4,0), (4,1)} R2 = {(1, 2), (2, 2), (3,0), (3,2), (4,0), (4,3)} R3 = {(0,0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} Which of these three relations is an...
ANSWER 2 & 3 please. Show work for my understanding and
upvote. THANK YOU!!
2. Given a regular n-gon, let r be a rotation of it by 2π/n radians. This time, assume that we are not allowed to flip over the n-gon. These n actions form a group denotecd (a) Draw a Cayley diagram for Cn for n-4, n-5, and n-6 (b) For n 4, 5, 6, find all minimal generating sets of C.· [Note: There are minimal generating sets...
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