Logic Principles: Sentence Connectives - & and V

SENTENCE CONNECTIVES “and” AND “or”

& = and

V = or

Commutative

Conjunctions   &  - commutative – you can reverse the position of the sentences joined by a conjunction and the truth values of the sentence remains the same.  For example, p & q has the same truth value as q & p.

Disjunctions p V q - commutative – you can reverse the position of the sentences joined by a conjunction and the truth values of the sentence remains the same.   For example, p V q has the same truth value as q V p.

Associative

Conjunctions are associative – you can change the order in which the compounds of the sentences joined by a conjunction are created and the truth values of the sentence remains the same.  For example,   (p & q) & r has the same truth value as p & (q & r).

Disjunctions are associative – you can change the order in which the compounds of the sentences joined by a disjunction are created and the truth values of the sentence remains the same.  For example,   (p V q) V r has the same truth value as p V (q V r).

Distributive

Conjunctions are distributive over disjunctions, as follows.  For example,   p & (q V r) has the same truth value as (p & q) V (p & r).

Disjunctions are distributive over conjunctions, as follows.  For example,   p V (q & r) has the same truth value as (p V q) & (p V r).