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. Approach: Here, R, F, L, B, T and U denotes the rotation of the Rubik’s cube 90 ∘ clockwise to the right, front, left, back, top, and under faces, respectively. The 90 ∘ clockwise rotation position of Rubik’s cube of R, F, L, B, T and U is given below. Convert the Rubik’s cube into standard position by making the given rotation in reverse order and reverse direction. Calculation: Prove that each move on the Rubik’s cube has an inverse move by using the definition mentioned above. Every element in G has an inverse g − 1 . That is, g * g − 1 = g − 1 * g = e

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 12.4, Problem 54PS

To determine

To find:

Each move on the Rubik’s cube has an inverse move.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.4, Problem 53PS

Chapter 12.4, Problem 55PS

Students have asked these similar questions

You may need to use the appropriate appendix table or technology to answer this question. You are given the following information obtained from a random sample of 4 observations. 24 48 31 57 You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 49. (Assume the population is normally distributed.) (a) State the null and the alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: (b) Determine the test statistic. (Round your answer to three decimal places.) (c) Determine the p-value, and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 49. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is insufficient evidence to conclude that the mean of the population is different from 49.Do not reject H0. There is sufficient evidence to conclude that the…

No chatgpt pls

Chapter 12 Solutions

Nature of Mathematics (MindTap Course List)

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.

Each move on the Rubik’s cube has an inverse move.

Solution Summary: The author explains that each move on the Rubik's cube has an inverse move.

Concept explainers

Videos

To find: Each move on the Rubik’s cube has an inverse move.

Want to see the full answer?

Chapter 12 Solutions

To find:

Each move on the Rubik’s cube has an inverse move.