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Propositional logic is the study of the truth or falsity of statements. It primarily deals with compound statements, that is, statements that are comprised of smaller, simpler propositions. A proposition is a description of a state of affairs that may be either true or false but not both. The truth value of a proposition is "true" if the proposition is true and "false" if the proposition is false. Connectives are the structures that combine these component propositions to make compound statements. Truth Table Constructor supports 6 connectives. They are as follows:
| Type | Connective | Statement Form |
| Negation (not) | ~, ! | ~P |
| Conjunction (and) | &, ^ | P & Q |
| Disjunction (or) | v | P v Q |
| Conditional (if-then) | =>, -> | P => Q |
| Biconditional (iff) | <=>, <-> | P <=> Q |
| Exclusive-or | + | P + Q |
In order to graphically show how these connectives work, it is necessary to use a truth table. A truth table is a means of showing all the possible combinations of true and false for the component propositions and the corresponding truth value of the compound statement. The following sections explain how each connective functions in propositional logic, and they provide the truth table for that particular connective.
Negation: reverses the truth value of a proposition.
| Negation: | |
Conjunction: the statement is true if and only if each component proposition is true.
| Conjunction: |  |
Disjunction: the statement is false if and only if each component proposition is false.
| Disjunction: |  |
Conditional: the statement is false if and only if the antecedent (the "if" part of the statement) is true and the consequent (the "then" part) is false.
| Conditional: |  |
Biconditional: the statement is true if and only if the two component propositions have the same truth value.
| Biconditional: |  |
Exclusive-or: the statement is true if and only if the two component propositions have opposite truth values. The exclusive-or connective yields the same result as negating the equivalent biconditional statement.
| Exclusive-or: |  |
Definitions
A tautology is a statement that is true regardless of the truth values of its parts. In terms of a truth table, it is one where every row evalutes to "true". The opposite of a tautology is a contradiction, a statement that is always false regardless of the truth values of its parts. In terms of a truth table, it is one where every row evalutes to "false". The truth value of a conditional statement varies with the truth values of its constituent propositions, thus producing a truth table where some rows evaluate to "true" and others evaluate to "false".