MACM 101 - Propositional Connectives

Negation

The logical operation that takes a proposition and inverts its truth value, making true statements false and vice versa. Ex. `It is not true that at least one politician was honest’ Denoted by the symbol ¬

Conjunction

The logical operation that combines two propositions and returns true only if both propositions are true. Ex. `It is raining and it is cold.' Denoted by the symbol ^

Disjunction

The logical operation that combines two propositions and returns true if at least one of the propositions is true. Ex. `It is raining or it is cold.' Denoted by the symbol \/.

Implication

The logical operation that represents a conditional relationship between two propositions, where if the first proposition is true, then the second must also be true. Ex. `If it rains, then the ground will be wet.' Denoted by the symbol →.

Exclusive Or

The logical operation that combines two propositions and returns true if exactly one of the propositions is true, but false if both are true or both are false. Ex. `There is either a tiger in this room, or a lady’ Denoted by the symbol ⊕.

Biconditional

The logical operation that represents a relationship between two propositions, where both propositions are either true or false together. Ex. `It is either raining if and only if the ground is wet.' Denoted by the symbol ↔.

Converse

A form of implication, where the positions of the two propositions are switched. For example, the converse of "If A, then B" is "If B, then A."

Contrapositive

A form of implication, where the positions of. the propositions are switched, and they are introduced to the negation connective. For example, the contrapositive of “If A, then B” is “If B is not true, then A is not true.

Inverse

A form of implication, where the propositions are not switched, but are combined with the negation connective. For example the inverse of “If A, then B” is “If not A, then not B.”