Obviously, the fourth and sixth relations do not satisfy transitivity, and the other four do.

Through < 1, 1 >∈R 1,< 1,1> ∈R 1 (repeated twice) can be known.

Counterexample:

Extended data:

In logic and mathematics, if the following statement holds for all A, B and c ∈X, then the binary relation R on the set is transitive: "If A is related to B and B and C, then A is related to C .."

If both the definition domain and the value domain are finite sets, then the main theoretical basis of its research is the pigeon-cage principle (judging the sufficiency of a non-one-to-one correspondence function).

In the process of a change, it is assumed that there are two variables X and Y. If there is a unique Y corresponding to any X, it is said that X is an independent variable and Y is a function of X. The range of X is called the domain of the function, and the range of Y is called the domain of the function.

Baidu Encyclopedia-Transitivity