(Sequential Criterion for Continuity) Let (S₁, d₁) and (S2, d2) be metric spaces, and f: S₁ S₂ be a function. Show that f is continuous at the point c E S₁ if and only if for every sequence (xn) in S₁ that converges to c, the sequence f(xn) converges to f(c). (Please use the correct definitions to prove this theorem.)

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A: See the attachment.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…