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  1. Should there be a comma in "for all"-sentences? For example, is the comma in the following sentence correct?

For all b ∈ B, there is an a ∈ A such that f(a) = b.

  1. Suppose that one wants to start a sentence with "In most cases". Should there be a comma after that? For example, is the comma in the following sentence correct?

In most cases, (a + b)² = a² + b² is false.

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Above mentioned examples are correct. As "For all b ∈ B" and "In most cases" are the introductory clauses so they must have comma. For more explanation refer this website.

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