An equivalence relation ~ on A partitions into pairwise disjoint subsets called equivalence classes so that 1. Within each class, every pair relates 2. Between classes there is no relation i.e. [x] = {a (element) A | a~x} and given two equivalence classes [a] and [b], either [a] = [b] or [a] intersect [b] = the empty set

.An association of packets that use the same path through a network

The answer is 1308. The trick is to notice that (12)(9)=108 which differs from 109 by only one. Now just consider the set of equivalence classes in Nmod12. the LCM of 109 and 12 will be apart of the equivalence class 0, so for every integer n between 1 and 12, (n)(109) is apart of the equivalence class n. In conclusion, the LCM must be the product (12)(109).

In ordinary mathematics, only 25 can equal 25.

There are other answers if you consider equivalence classes, but even that will be a number belonging to the same equivalence class as 25 and with the same properties as 25, but not EQUAL to 25.

An equivalence modulo is a relation between elements of a set, where two elements are considered equivalent if they have the same remainder when divided by a fixed number called the modulus. For example, in modulo 5 arithmetic, the equivalence class of 2 would include all numbers that leave a remainder of 2 when divided by 5: {2, 7, 12, 17, ...}. Equivalence modulo is often used in number theory and modular arithmetic.