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Mathematical Logical Connectives
A Logical Connective is a symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.
Generally there are five connectives which are −
OR (∨)
AND (∧)
Negation/ NOT (¬)
Implication / if-then (→)
If and only if (⇔).
OR (∨) − The OR operation of two propositions A and B (written as A ∨ B) is true if at least any of the propositional variable A or B is true.
The truth table is as follows −
| A | B | A ∨ B |
|---|---|---|
| True | True | True |
| True | False | True |
| False | True | True |
| False | False | False |
AND (∧) − The AND operation of two propositions A and B (written as $A \land B$) is true if both the propositional variable A and B is true.
The truth table is as follows −
| A | B | A ∧ B |
|---|---|---|
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | False |
Negation (¬) − The negation of a proposition A (written as ¬ A) is false when A is true and is true when A is false.
The truth table is as follows −
| A | ¬ A |
|---|---|
| True | False |
| False | True |
Implication / if-then (→) − An implication A → B is the proposition “if A, then B”. It is false if A is true and B is false. The rest cases are true.
The truth table is as follows −
| A | B | A → B |
|---|---|---|
| True | True | True |
| True | False | False |
| False | True | True |
| False | False | True |
If and only if (⇔) − A ⇔ B is bi-conditional logical connective which is true when p and q are same, i.e. both are false or both are true.
The truth table is as follows −
| A | B | A ⇔ B |
|---|---|---|
| True | True | True |
| True | False | False |
| False | True | False |
| False | False | True |
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