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Section 2: Reflexivity, 10.2.1 Symmetry, and Transitivity
www.csee.umbc.eduSection 2: Reflexivity, Symmetry, and Transitivity • Definition: Let R be a binary relation on A. ... • Given the relation R on {1,2,3,4}, its transitive closure is: 1 2 4 3 1 2 4 3 10.2.5. Properties of Equality ... symmetry and transitivity are vacuously satisfied! 10.2.6. Properties of Congruence Mod p
Congruence and Congruence Classes
math.okstate.eduSo b a (mod n) and b c mod n). By the symmetry and transitivity properties of congruence we then have a c (mod n) : Hence [a] n = [c] n by Theorem 2.3. Corollary 11.14. There are exactly n distinct congruence classes modulo n; namely, [0], [1], [2], ::: ,[n-1]. Proof. We rst show that no two of 0;1;2;:::;n 1 are congruent modulo n. To see this ...