2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on Aand find the quotient set A.(a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁.(b) (a,b) = (a₁, b₁) if ab = a₁b₁.(c) (a, b) = (a₁, b₁) if a = a₁.(d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.

Given Information: and There are four different types of relations given.To find: is an Equivalence…

Answered: Let U = {1, 2, 3} and A = U × U. In…

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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11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.
Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 = %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is, x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.
Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3),(4,5)} on the set A = {1,2,3,4,5,6}. Find the Symmetric and reflexive closure.
Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c), (c, d), (d, d)} be arelation on A. Which of the properties reflexive, symmetric and transitive does the relation R possess? If Rdoes not possess one of these properties, explain why. How do I know where to stop? How do I know when I have proven transitivity? for example? I have difficulties with knowing if my prove is complete or not
11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.
Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A={1,2,3}. Select one: O a. ={(2,2),(3,1),(2.2).(2,3).(3,3)}. O b. ={(1,1),(3,1),(2.2),(2,3),(3,3)}. O c. =((1,3),(3,1).(2,2), (2,3),(3,3)}. O d. ={(1,2),(1,3).(2,2),(2,3),(3,3)}. O e. ={(1,2),(3,1),(2,2),(2,3),(3,3)}.
11./ a) b) c) 11 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine if the relation is reflexive. If it is not reflexive, state why. Determine if the relation is symmetric. If it is not symmetric, state why. Sketch a digraph to represent the relation.
For the relations: A x B, such that: A = {37, 38, ..., 42} and B = {42, 43,..., 47} Count how many possible ways N₁ to have functions P: A B N₁ = Count how many possible ways N₂ to have as one-to- one function N₂ = Count how many possible ways N3 to have y NOT onto. N3 =
Let A={1,2,3,4}, B={1,3}, and the relations R1: a
Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3)} on the set A = %3! {1,2,3,4,5}. Find the Symmetric and reflexive closure.

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Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a,b) = (a₁, b₁) if a = a₁. (d) (a,b) = (a₁, b₁) if a − b = a₁ − b₁.