For each of the following relations, determine whether the relation is reflexive

Question

For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. R Z+ times Z+ where a R b if a|b (read "a divides b." as defined in Section 4.3). R is the relation on Z where a R b if a|b. For a given universe U and a fixed subset C of U. define R on R as follows: For A, B U we have A R B if A C = B C. On the set A of all lines in R2 , define the relation R for two lines l1 , l2 by l1 R l2 if l1 is perpendicular to l2. Which relations in Exercise 5 are partial orders? Which are equivalence relations?

Explanation / Answer

a , c are equivalance relations

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