Given the sets A = {a, b, c, d}, B = {0, 1, 2, 3} construct a relation R such that R is an injective function and R^−1 is a surjective function. Represent R and R^−1 with graphs. How many different equivalence relations with exactly 3 different equivalence classes are there on a set with 5 elements? [Hint: partitions]

Given the sets A = {a, b, c, d}, B = {0, 1, 2, 3} construct a relation R such that R is an injective function and R^−1 is a surjective function. Represent R and R^−1 with graphs. How many different equivalence relations with exactly 3 different equivalence classes are there on a set with 5 elements? [Hint: partitions]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

See similar textbooks

Similar questions

Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on theset {1, 2, 3, 4} that is reflexive, symmetric and transitive.
Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have the same cardinality?
(1) Prove that the relation is an equivalence relation, and(2) Describe the distinct equivalence classes of reach relation.
Which of these ordered pairs belongs to the "does not divide" relation on the set of positive integers, where (a, b) belongs to this relation if a and b are positive integers such that a does not divide b? (Select all that apply.)
Consider a set A with 10 elements. How many different functions are there from the set A to a set with three elements?
Determine whether the relation R on the set of all people is reflexive,symmetric, antisymettric and/or transitive where (a,b) ∈ R if and only if 1. a is taller than b. 2. a and b born on same day. 3. a has the first name as the b. a and b have a common grandparent. Which of the above relations on the set of all people are equivalence relations and/or partial order relation?
Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b), how do you determine when to stop? please show the steps to get the equivalence classes in detail, thank you in advance.
Let ∼be the equivalence relation on R defined by x∼y if and only if ⌊x⌋=⌊y⌋. Using interval notation, describe the equivalence class of 15
Let R be a relation over a set A = {a,b,c,d}. What kind of order is R? Note: Select the order that it satisfies the most properties for. That is, if the relation is a partial order, then it's also technically a preorder; but partial order will be correct, and preorder will be an incorrect response. If the relation doesn't satisfy all of the properties for any of the listed orders, then select "None of these". R = {(a,a), (b,b), (c,c), (d,d), (a,b), (c,d), (a,c), (b,c), (a,d), (b,d)}