connected said of a relation R where, for any two distinct elements x and y of the domain, either xRy or yRx. R is said to be strongly connected if, for any two elements x and y, either xRy or yRx, even if x and y are identical. Given the domain of positive integers, for instance, the relation ‹ is connected, since for any two distinct numbers a and b, either a ‹ b or b ‹ a. ‹ is not strongly connected, however, since if a % b we do not have either a ‹ b or b ‹ a. The relation o, however, is strongly connected, since either a o b or b o a for any two numbers, including the case where a % b. An example of a relation that is not connected is the subset relation 0, since it is not true that for any two sets A and B, either A 0 B or B 0 A. See also RELATION. V.K.