View S3 as a subset of S5 in the obvious way. For σ, τ ∈ S5,...

View S₃ as a subset of S₅ in the obvious way. For σ, τ ∈ S₅, define σ ∼ τ if στ ^-1 ∈ S₃.

(a) Prove that ∼ is an equivalence relation on S5.

(b) Find the equivalence class of (4, 5).

(c) Find the equivalence class of (1, 2, 3, 4, 5).

(d) Determine the total number of equivalence classes

Expert Solution

Colby Messinger answered 2 years ago

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