1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).

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A: Step 1:Step 2:Step 3:Step 4:Here 2 mod 3= 1 and −1 mod 3= 2.−2 mod 2= 0 and −1 mod 2= 1.

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A: If you have any help please let me know in comment box thankyou.

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A: From the matrices A and B :A=⎝⎛​8111​72−8​−501​⎠⎞​B=⎝⎛​111​584​203​01−6​⎠⎞​Matrix multiplication:…

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A: More explain

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Q: PROBLEM 2 Let σ, TEST be defined by the formulae 1 2 3 4 5 6 7 στ 5 4 1 6723 and T = (6 1)(5 1)(4…

A: 2.1 Let's find the cycle decompositions and orders of σ, τ, and στ.For σ = (1 2 3 4 5 6 7) (5 4 1 6…