Let X be a finite set. For subsets A, BEP(X), let ARB if |A| = |B|. This is an equivalence relation on P(X). If x= {1, 2, 3), list the equivalence classes. (Select all that apply.) {{1}, {2}, {3}} {{2, 3}, {1}} {{1, 2, 3}, {1}, {2}, {3}} {{1, 2, 3}} {{1, 3}, {2}} ☐ {0} {{1, 2}, {3}} {{1, 2}, {2, 3}, {1, 3}}

Let X be a finite set. For subsets A, BEP(X), let ARB if |A| = |B|. This is an equivalence relation on P(X). If x= {1, 2, 3), list the equivalence classes. (Select all that apply.) {{1}, {2}, {3}} {{2, 3}, {1}} {{1, 2, 3}, {1}, {2}, {3}} {{1, 2, 3}} {{1, 3}, {2}} ☐ {0} {{1, 2}, {3}} {{1, 2}, {2, 3}, {1, 3}}

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Let A be a non-empty set, ≃ ⊆ A × A an equivalence realtionship and ⪯ ⊆ A × A a partial order, both over A. Consider the quotient set: A / ≃, and define the following relation ≪ ⊆ (A/ ≃) × (A/ ≃) where (S1, S2) ∈ ≪ if, and only if, there is an a ∈ S1 such that for all b ∈ S2, a ⪯ b. 1.) How to show that ≪r is is a partial order over A/ ≃ where ≪r is the reflex cause of ≪. 2.) Is it true that A has a minimal element according to ⪯ if, and only if, A/ ≃ has a minimal element according to≪r ? How to show if it is true or false (in such case suggest a counterexample)
Prove that equivalences of sets are transitive, for example if X ~ Y and Y ~ Z then X ~ Z.
Implement the following Racket functions: Reflexive-Closure Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S, Reflexive-Closure should return the reflexive closure of L. In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R. (https://en.wikipedia.org/wiki/Reflexive_closure) Examples: (Reflexive-Closure '((a a) (b b) (c c)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (b b)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (a b) (b b) (b c)) '(a b c)) ---> ((a a) (a b) (b b) (b c) (c c)) (Reflexive? '() '(a b c)) ---> '((a a) (b b) (c c)) You must use recursion, and not iteration. You may not use side-effects (e.g. set!).
Let S be a set and let C = (π1, π2,...,πn) be an increasing chain ofpartitions (PART(S), ≤) such that π1 = αS and πn = ωS. Then, the collection HC = ni=1 πi that consists of the blocks of all partitions in the chain is a hierarchy on S.
) Let O be the set of odd numbers and O’ = {1, 5, 9, 13, 17, ...} be its subset. Definethe bijections, f and g as:f : O 6 O’, f(d) = 2d - 1, d 0 O.g : ø 6 O, g(n) = 2n + 1, n 0 ø.Using only the concept of function composition, can there be a bijective map from øto O’? If so, compute it. If not, explain in details why not...................................................................................................................................... [2+8]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 xbegins with the same letter as y.Determine whether or not this is an equivalence relation.If it is an equivalence relation then1. 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
Assume a generic recursive relation is defined as : A[i] = p*A[i-1] + q where p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list, such as [A[0], A[1], A[2]] and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series: A[i] = A[i-1] + 2 where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case. Phyton
Assume a generic recursive relation is defined as : A[i] = p*A[i-1] + q where p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list, such as [A[0], A[1], A[2]] and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series: A[i] = A[i-1] + 2 where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case. """ def recursionSolver(values): return # Remove this line to answer this question.
Let the Universal set be {a,b,c,d,e,f,g,h,i,j] Consider the subsets A = {a,d,h,i} B= {b,c,d.,f,i,j} C = {a,c,e,f,g,} What is (An B' )'?
Let R ⊆ A × A be a a binary relationship defined in a non-empty set A. Let B be any set so that B⊆ A. Define the set Rb as RB := R ∩ (B × B). 1.) How to show that if R is reflexive, symmetric and transitive then Rb also is. 2.) Is the opposite true? Demonstrate truth or falseness. 3.) If R is antisimetric, is Rb antisimetric too?
Assume a generic recursive relation is defined as :A[i] = p*A[i-1] + qwhere p and q are coefficients of the relation. Write a function that takes the first three numbers in this relation as a list,such as [A[0], A[1], A[2]]and computes p and q, and returns A[3]. For example, given [1,3,5] your function should return 7, because the numbers 1,3,5 are produced by the series:A[i] = A[i-1] + 2where p is 1 and q is 2, and then the next number in the series becomes 7. You can assume that p and q are always integers. You can also assume that p and q are determinable in any test case.""" def recursionSolver(values):return # Remove this line to answer this question. İn python.
Show that property (3) of a matroid implies: For any S ∈ I, {x} ∈ I, there exists y ∈ S, such that S \ {y} ∪ {x} ∈ I.
On S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:xRy , x divides y:(i) Find all non-empty subsets U S, so that 6 is an R-lowerbound of U.(ii) Let A = f6; 10; 12g. If A admits an R-supremum, nd it. If A admits an R-in mum, nd it.(iii) Is R a lattice?