华东师范大学《软件工程数学》第八章作业.doc

2. a) List all the ordered pairs in the relation R= {( a,b)|a divides b} on the set {I, 2,3,4,5,6 } . 3. For each of these relations on the set {1, 2, 3, 41, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(I, 1), (1, 2), (2,1), (2, 2), (3, 3), (4,4)} c) {(2, 4), (4, 2)} d) {(I, 2), (2, 3), (3,4)} e) {(I, 1),(2,2),(3,3),(4,4)} f) {(I, 3), (1,4), (2, 3), (2,4), (3,1), (3, 4)} 6. Determine whether the relation R on the set of all real numbers is reflexive, symmetric, anti symmetri c, and/or transitive, where ( x, y)∈R if and only if a)x+y=0 b)x=± y. c)x-y isa rational number. d)x= 2y. e) xy≥ o. f) xy= 0. g)x= 1. h)x=1 ory= 1. 8. Give an example ofa relation ona set that is a) symmetric and antisymmetric. b) neither symmetric nor anti symmetric. 12. Which relations in Exercise 6 are irreflexive? 24. Let R be the relation R= {( a,b)|a<b} on the set of integers. Find a)R -1. b)R . 28. Let R 1= {(1, 2), (2, 3),(3,4)} and R 2= {(1,1), (1,2), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (3,4)}be relations from {1, 2, 3} to {1, 2, 3,4}. Find a)R 1∪R 2. b)R 1∩R 2. c)R 1-R 2. d)R 2-R 1. 30. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3,1)}, and letS be the relation {(2, 1), (3, 1), (3, 2), (4, 2)}. Find SoR. 32. Find 38. Let R 1 and R 2 be th