Discrete mathematics problem, let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove Let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove that if R is an equivalence relation on a, then s is also an equivalence relation, and S = R It's OK to connect~

Discrete mathematics problem, let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove Let R be a binary relation on a, define s = {(a, b) | &; C ∈ a, (a, c) ∈ R, (C, b) ∈ r}, prove that if R is an equivalence relation on a, then s is also an equivalence relation, and S = R It's OK to connect~

Because R is an equivalent relation on a, a has Reflexivity on R, &; C ∈ a, (a, c) ∈ R, (C, b) ∈ R, so in the set s, &; C ∈ a (C, c) ∈ R, then s has Reflexivity on A. A has symmetry on R, &; C ∈ a, (a, c) ∈ R, (C, b) ∈ R (implied a, B is also on the set a), then s has Reflexivity on a, a) The symmetry of ∈ s a on S is also due to the transitivity of R, &; C ∈ a, (a, c) ∈ R, (C, b) ∈ R (implied a, B is also on the set a), so it is easy to know that s also has symmetry. S satisfies the above three properties, which is also the equivalence relation on a. the above description shows that every ordered pair on a is also on S, so s = R