For example, the operation of "addition" and the set of real numbers R, we all know that for any two elements in R, that is, two real numbers, the result obtained after their addition operation must still be real numbers. At this time, we say that the real number set R is closed for the operation "addition". In fact, closure means that after the elements in the R set are "added", the result is still the elements of this set, that is, these elements are closed inside the set.

Now let's talk about how to verify whether a set is closed for the operation @ in the topic.

(1) is not closed: only two elements need to be found, and the @ operation results of these two elements are not in the set.

(2) Closure: Verify that any two elements (the word arbitrary is very important) are still in the collection after @ operation.

You say m 1.m2.n 1.n2 to show that x 1, X2 is arbitrary, so mark 1, 2 to distinguish them?

Please see the picture below for the answer to the question.