Read the textbook carefully, and the definition of communication is: if there is.

Let's describe this definition in another way: if there are two ordered pairs in R that can be inherited, then the inheritance must be complete. Simply put, it is "pass it on if you can!" (on the other hand, if there is no premise of transmission, that is, A is false, then A->; B is true and transitive)

If you still don't understand, let's put it another way: if X can find Y and Y can find Z, then theoretically X should also find Z, which is called transitivity.

Look at two examples (let a be {1, 2,3}):

I. r = {

We think this relationship is not transitive! Why? What can be delivered is not completed (1 can find 2, 2 can find 3, so 1 should also find 3, but it is not.

Second, r = {

It is transitive! Because everything that can be transmitted has arrived. (No ordered pair can inherit, 1 can find 2, but 2 can't find other elements)

Third, {

Without transitivity, 1 can find 2, and 2 can find 1, so after inheritance, 1 will also find 1 (isn't it strange to find yourself? For example, 2 can also be found in the same way, so {< 1, 2 >; ，& lt2， 1 & gt； ，& lt 1， 1 & gt； ，& lt2，2 & gt； } is transitive. Note: x, y and z in the definition should not be different elements, such as x=z= 1 and y=2 in this example.

Fourth, {

It is transitive. What if x=y=z= 1? 1 find 1, 1 find 1, so 1 can find 1! (2, 3 similar)

Logical things are more troublesome, but it will be very simple after you figure it out.