Each logical connective can be expressed as a function, called a truth function. For this reason, logical connectives are sometimes called truth-functional connectives. The most common logical connectives are binary connectives which join two sentences whose truth values can be thought of as the function's operands.
Logical connectives along with quantifiers are the two main types of logical constants used in formal systems such as propositional logic and predicate logic.
TYPES
Negation (not) (¬ or ~)
Negation is an operation on one logical value, trypically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true.
| p | ¬p |
|---|---|
| True | False |
| False | True |
Conjunction (and) (
, &, or · )Conjunction is an operation on two logical values, trypically the values of two propositions that produces a value of true if and only if both of its operands are true.
Truth table of p^q
| p | q | p ∧ q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
or ∨ )Disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false.
Truth table of p∨q
| p | q | p ∨ q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
, 
or 
)Implication and conditional are both associated with an operation on two logical values, typically the values of two propositions, that produces a value of false just in case the first operand is true is true and the second operand is false.
Truth table of p → q
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
)Biconditional is an operation on two logical values, typically the values of two logical values, typically the values of two propositions, that produce a value of true if and only if both operands are false or both operands are true.
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