Consider the following input to the stable matching problem with n=3 men (X, Y, Z)and women (A, B, C), and their preferencesA: X>Y > ZB:X > Y > ZC: Z>Y > XX: C> A > BY: A > B> CZ: A > B>CConsider the matching (A,Z), (B,X) and (C,Y).Select all the pairs that form an instability (where pair (m,w) form an instability if mprefers w over their partner in the matching AND w prefers m over their partner inthe matching.) a) (A,X) form an instabilityb) (A, Y) form an instabilityc) (A, Z) form an instabilityd) (B,X) form an instabilitye) (BY) form an instabilityf) (B,Z) form an instabilityg) (C,X) form an instabilityOh) (C,Y) form an instabilityi) (C,Z) form an instabilityOj) there are no instabilities

Firstly, we will create preference matrices for both men and women.

Answered: Select all the pairs that form an…

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Select all the pairs that form an instability

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

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Question

Consider the following input to the stable matching problem with n=3 men (X, Y, Z)
and women (A, B, C), and their preferences
A: X>Y > Z
B:X > Y > Z
C: Z>Y > X
X: C> A > B
Y: A > B> C
Z: A > B>C
Consider the matching (A,Z), (B,X) and (C,Y).
Select all the pairs that form an instability (where pair (m,w) form an instability if m
prefers w over their partner in the matching AND w prefers m over their partner in
the matching.)

a) (A,X) form an instability
b) (A, Y) form an instability
c) (A, Z) form an instability
d) (B,X) form an instability
e) (BY) form an instability
f) (B,Z) form an instability
g) (C,X) form an instability
Oh) (C,Y) form an instability
i) (C,Z) form an instability
Oj) there are no instabilities

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