21127 Lecture Notes - Lecture 16: Bes, Seta
Document Summary
Overall, we were very happy with how well you did on the exam! Remember that regrade submissions are due on monday. Read the part about relations and equivalence relations over the weekend. (skip the part about order relations. ) Relations and properties: de ne the relation r on {a, b, c} by. R = {(a, a), (a, c), (b, c), (c, b)} This is re exive, symmetric, and transitive: de ne the relation on p(n) by saying, for any x, y n, For example, {1} {1, 2, 3} and {1, 2, 3} {1, 2, 3, 4, 5} and {1, 2, 3} {5, 6, 7}, but {1, 2, 3} (cid:54) . This is re exive, not symmetric, and not transitive. An equivalence relation is a relation that is re exive, symmetric, and transitive. The idea is that an equivalence relation packages the underlying set into pieces. Example 0. 1. on the set r, de ne r to be the relation where.