Let A be a set, B a subset of A, and let b be one particular element

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Let A be a set, B a subset of A, and let b be one particular element of B. Determine whether the given set is sure to be a subgroup of SA under the induced operation. Here σ[B] = {σ(x) |x ∈ B}.

{σ ∈ SA |σ(b) ∈ B}

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