Commutativity

A rule of inference in propositional logic. Written 'com.' for short. It goes like this:

(P∨Q) = (Q∨P)
And
(Q∧P) = (P∧Q)

"I have an apple or an orange" is the same as "I have an orange or an apple".
And...
"I have an apple and an orange" is the same as "I have an orange and an apple".

A very simple and intuitive rule, but logicians like to be very precise.

Back up to Rules of Inference
Review your Logic symbols

A property that some binary operations possess. The operation @ is commutative if for all a,b, the following holds:

a@b = b@a

Examples:

• addition, XOR
• multiplication
• max (including logical OR)
• min (including logical AND)
• Define a#b to be the number of appearances of 42 among a,b. It is easy to verify # is commutative. But it lacks associativity, which shows (along with, say, matrix multiplication) that there is no connection between the two concepts.

Non examples:

• subtraction
• division
• matrix multiplication
• exponentiation