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

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 12.4, Problem 56PS

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To prove:

The move L−1R−1 is the reverse move of LR and the L−1R−1 is the reverse move of RL.

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Chapter 12.4, Problem 55PS

Chapter 12.4, Problem 57PS

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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

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To prove: The move L − 1 R − 1 is the reverse move of L R and the L − 1 R − 1 is the reverse move of R L .

Solution Summary: The author explains that the binary operator * is a sequence of cube’s move or rotation of.

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To prove:

The move L−1R−1 is the reverse move of LR and the L−1R−1 is the reverse move of RL.

Want to see the full answer?

Chapter 12 Solutions

To prove: The move L − 1 R − 1 is the reverse move of L R and the L − 1 R − 1 is the reverse move of R L .

Solution Summary: The author explains that the binary operator * is a sequence of cube’s move or rotation of.

Concept explainers

Videos

To prove: The move L−1R−1 is the reverse move of LR and the L−1R−1 is the reverse move of RL.

Want to see the full answer?

Chapter 12 Solutions

To prove:

The move L−1R−1 is the reverse move of LR and the L−1R−1 is the reverse move of RL.