Logical operator

In a logical calculus, logical operators serve to connect terms into expressions. If you have two terms, A and B, standing for the assertion?s "It's raining", and "I'm inside", respectively, these terms can be combined into compound assertions, like "it's raining, and I'm inside" or "if it's raining, then I'm inside."

The basic operators are "not?" (¬), "and" (∧), "or?" (∨), "conditional?" (→), and "biconditional?" (↔). "Not" is a unary operator--it takes a single term ( ¬ A ). The rest are binary operators, taking two terms to make a compound statement ( A ∧ B, A ∨ B, A → B, A ↔ B ).

Note that the [logical equivalence]? of certain compound statements entails that not all of these operators are necessary for a full-blooded logical calculus. For example, ¬ A ∨ B is logically equivalent to A → B; since logical equivalence means that equivalent terms may be subsituted for each other in an expression, it's not necessary to have a conditional operator. A common exercise in introductory classes in symbolic logic is to define a single operator, from which all five operators can be derived through equivalence (the most common means of defining an operator is by describing its truth table). The five operators listed above are the basic set for the sake of convenience (and brevity).