Settling time
In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic. It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition.[1]
Formal notation
Commutativity of conjunction can be expressed in sequent notation as:
and
where is a metalogical symbol meaning that is a syntactic consequence of , in the one case, and is a syntactic consequence of in the other, in some logical system;
or in rule form:
and
where the rule is that wherever an instance of "" appears on a line of a proof, it can be replaced with "" and wherever an instance of "" appears on a line of a proof, it can be replaced with "";
or as the statement of a truth-functional tautology or theorem of propositional logic:
and
where and are propositions expressed in some formal system.
Generalized principle
For any propositions H1, H2, ... Hn, and permutation σ(n) of the numbers 1 through n, it is the case that:
is equivalent to
For example, if H1 is
- It is raining
H2 is
- Socrates is mortal
and H3 is
- 2+2=4
then
It is raining and Socrates is mortal and 2+2=4
is equivalent to
Socrates is mortal and 2+2=4 and it is raining
and the other orderings of the predicates.
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534