Logical connective
A logical connective (also called a logical operator, sentential connective, or propositional connective) is a symbol or word used to connect two or more propositions in a logical formula to form a compound proposition. Logical connectives are fundamental to the field of propositional logic and are used to build complex logical expressions from simpler ones.
Types of Logical Connectives[edit | edit source]
Logical connectives can be classified into several types based on their function:
- Conjunction (AND, ∧): The conjunction of two propositions is true if and only if both propositions are true.
- Disjunction (OR, ∨): The disjunction of two propositions is true if at least one of the propositions is true.
- Negation (NOT, ¬): The negation of a proposition is true if the proposition is false.
- Implication (IF...THEN, →): The implication is true if the first proposition implies the second proposition.
- Biconditional (IF AND ONLY IF, ↔): The biconditional is true if both propositions are either true or false.
Truth Tables[edit | edit source]
Logical connectives are often defined using truth tables, which show the truth value of a compound proposition for every possible combination of truth values of its components.
Conjunction (AND)[edit | edit source]
| P | Q | P ∧ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Disjunction (OR)[edit | edit source]
| P | Q | P ∨ Q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Negation (NOT)[edit | edit source]
| P | ¬P |
|---|---|
| T | F |
| F | T |
Implication (IF...THEN)[edit | edit source]
| P | Q | P → Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Biconditional (IF AND ONLY IF)[edit | edit source]
| P | Q | P ↔ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
Applications[edit | edit source]
Logical connectives are used in various fields such as mathematics, computer science, philosophy, and linguistics. In computer programming, logical operators are used to control the flow of execution and to perform logical operations on data.
Related Pages[edit | edit source]
- Propositional logic
- Truth table
- Boolean algebra
- Predicate logic
- Logical equivalence
- Logical consequence
See Also[edit | edit source]
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