Connective | Example | Alternative Symbols |
---|---|---|
Negation | ||
Disjunction (or) | ||
Conjunction (and) | ||
Conditional (implies) | ||
Biconditional (equivalent) | ||
Exclusive Or |
Order of Precedence and Associativity
Both conjunction and disjunction are associative, so we can write something like
To further reduce the number of necessary parentheses, some sources introduce precedence rules for connectives. For the big 5 connectives in propositional logic, we can define precedence and associativity as follows, with operators at the top having higher precedence
Operator |
---|
Some sources also define
Truth Functional Connectives
A connective is truth functional if the truth-value of the compound proposition is entirely determined by the truth values of component propositions.
All the above connectives are truth functional. But we can have non-truth functional connectives if we use casual English. For example, unlike