Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher logics. Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers. Propositional variables are the atomic formulas of propositional logic. For example, in a given propositional logic, we might define a formula as follows: Every propositional variable is a formula. Given a formula X the negation ¬X is a formula. Given two formulas X and Y, and a binary connective b (such as the logical conjunction ), then (X b Y) is a formula.

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