Example: R is a reflexive relation on the set X. it is proved that R is symmetric and transitive if and only if There is a difference between a, b > and in R Example: let R 1 and R 2 be two equivalence relations in set a, and R 1, R 2 = R 2, R 1, R 2 is also the equivalence relation on a Proof: 1) reflexivity (omitted) 2) Symmetry (omitted) 3) Transitivity: If, then And, so, so And then by and by transmission, we get, Again by knowing, so, so, again by and is transmitted, get, and so Example: let R be a reflexive transitive binary relation on set a, and let t also be a binary relation on set a, and satisfy the following conditions: . prove: t is the equivalent relation on a

Example: R is a reflexive relation on the set X. it is proved that R is symmetric and transitive if and only if There is a difference between a, b > and in R Example: let R 1 and R 2 be two equivalence relations in set a, and R 1, R 2 = R 2, R 1, R 2 is also the equivalence relation on a Proof: 1) reflexivity (omitted) 2) Symmetry (omitted) 3) Transitivity: If, then And, so, so And then by and by transmission, we get, Again by knowing, so, so, again by and is transmitted, get, and so Example: let R be a reflexive transitive binary relation on set a, and let t also be a binary relation on set a, and satisfy the following conditions: . prove: t is the equivalent relation on a

Discrete mathematics is almost forgotten. Example: R is a reflexive relation on set X. proof: R is symmetric and transitive if and only if < A, b > and in R are in R. proof: 1) sufficiency: suppose R is symmetric and transitive. R is symmetric, and ∈ r = > ∈ RR is transitive, and ∈