MATH 221 Quiz: MATH 221 Drexel Quiz10 Solutions
Document Summary
For each of these relations on the set {1, 2, 3, 4}, decide whether it is re exive, whether it is symmetric, whether it is anti- symmetric, and whether it is transitive. Which of these relations are equivalence relations? (a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}. (b) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}. (c) {(2, 4), (4, 2)}. Solution. (a) not re exive: (4, 4) is missing (and therefore this is not an equivalence relation). Not symmetric: (2, 4) belongs to the relation, and (4, 2) does not. Not antisymmetric: both (2, 3) and (3, 2) belong to the relation and 2 6= 3. Transitive. (b) re exive, symmetric transitive, and therefore this is an equiva- lence relation.
