B

Therefore, C.

where A, B, and C, are variables that can take as values any sentences including those that in turn contain connectives.

Logicians can set up the proof theory for a calculus in various ways. They can formalize the sentential calculus, for example, using just a single rule of inference and a set of axioms, which are assertions that are assumed to be true. However, a more intuitive method, known as natural deduction, dispenses with axioms in favor of formal rules of inference for negation and for each of the sentential connectives. Certain rules introduce connectives into a proof, such as the rule that introduces "and," using it to conjoin two premises:

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