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How did Frege analyze words such as “and” and “not” as logical functions?

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Gottlob Frege analyzed sentential connectives such as "and" and "not" by treating them as logical functions that produce new truth-values when applied to other sentences as arguments.1

In this framework, Frege viewed these connectives as analogous to mathematical functions. Just as a mathematical function takes a numerical input to produce a specific output, these logical functions take the truth-values of component sentences to determine the truth-value of the resulting complex sentence. For example, the function corresponding to "not" (negation) takes a true sentence and produces a false one, or vice versa.12

While Frege was aware of the concept of treating these connectives as truth-functions, this approach was later emphasized most strongly by Ludwig Wittgenstein. By isolating these functions, Frege was able to determine the truth-value of an entire sentence based on the outputs of its constituent parts, a method that became foundational to modern propositional calculus.21