Explanation Definition: The binary operator * is a sequence of cube’s move or rotation of a cube face. Eliminate the symbol * . For example, here interpret F B as F * B . This operation has inverse property. Group condition of Rubik’s cube: A group G consists of a set of objects and the binary operator * on those objects satisfying the following conditions. Closure property: The operation * is closed, so any elements h and g in G, h * g is also in G. Associative property: The operation * is associative, so any elements f, g and h in G, then ( f * g ) * h = f * ( g * h ) . Identity property : There is an identity element e ∈ G such that e * g = g * e = g . Inverse property : Every element in G has an inverse g − 1 relative to the operation * such that g * g − 1 = g − 1 * g = e . Commutative property: The set of n × n non-singular matrices from a group under multiplication is an example of non-commutative group or non-abelian group and it is also known as Rubik group

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

13th Edition

ISBN: 9781337605076

Author: karl J. smith

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

Videos

Question

Chapter 12.4, Problem 53PS

To determine

To find:

The Rubik’s cube is associative for three consecutive moves M1, M2 and M3, that is M1(M2M3)=(M1M2)M3.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 52PS

Chapter 12.4, Problem 54PS

Students have asked these similar questions

The everything combined problem Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. 1. How many cables would you need to connect each station to each server? 2. How many stations can be used at one time? 3. How many stations can not be used at any one time? 4. How many ways are there to pick 10 stations out of 15? 5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can simultaneously access different servers via direct connections. What is the minimum number of direct connections needed to achieve this goal?

Can you help me with D and E

Q1.1 1 Point Any set {V1, V2, V3, V4} that consists of four different vectors from R cannot possibly span Rº. True False Save Answer

Chapter 12 Solutions

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The Rubik’s cube is associative for three consecutive moves M 1 , M 2 and M 3 , that is M 1 ( M 2 M 3 ) = ( M 1 M 2 ) M 3 .

Solution Summary: The author explains that the Rubik's cube is associative for three consecutive moves.

Concept explainers

Videos

To find:

The Rubik’s cube is associative for three consecutive moves M1, M2 and M3, that is M1(M2M3)=(M1M2)M3.

Want to see the full answer?

Chapter 12 Solutions

The Rubik’s cube is associative for three consecutive moves M 1 , M 2 and M 3 , that is M 1 ( M 2 M 3 ) = ( M 1 M 2 ) M 3 .

Solution Summary: The author explains that the Rubik's cube is associative for three consecutive moves.

Concept explainers

Videos

To find: The Rubik’s cube is associative for three consecutive moves M1, M2 and M3, that is M1(M2M3)=(M1M2)M3.

Want to see the full answer?

Chapter 12 Solutions

To find:

The Rubik’s cube is associative for three consecutive moves M1, M2 and M3, that is M1(M2M3)=(M1M2)M3.