# Mathematical Logical Connectives

MathematicsComputer EngineeringMCA

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 −

ABA ∨ B
TrueTrueTrue
TrueFalseTrue
FalseTrueTrue
FalseFalseFalse

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 −

ABA ∧ B
TrueTrueTrue
TrueFalseFalse
FalseTrueFalse
FalseFalseFalse

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
TrueFalse
FalseTrue

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 −

ABA → B
TrueTrueTrue
TrueFalseFalse
FalseTrueTrue
FalseFalseTrue

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 −

ABA ⇔ B
TrueTrueTrue
TrueFalseFalse
FalseTrueFalse
FalseFalseTrue