each of these relations on the set {1, 2, 3, 4}, 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) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} c) {(2,4),(4,2)} d) {(1, 2), (2, 3), (3, 4)} e) {(1, 1), (2, 2), (3, 3), (4, 4)} f) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 2), (3, 4)}
each of these relations on the set {1, 2, 3, 4}, 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) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} c) {(2,4),(4,2)} d) {(1, 2), (2, 3), (3, 4)} e) {(1, 1), (2, 2), (3, 3), (4, 4)} f) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 2), (3, 4)}
each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.
3) Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the
ordered pairs
(2,3),(3,2), (4, 7), (5, 5) and (8, 7)?
2. For each of these relations on the set {1, 2, 3, 4), 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) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)}
c) {(2, 4), (4, 2)}
d) {(1, 2), (2, 3), (3, 4)}
e) {(1, 1), (2, 2), (3, 3), (4,4)}
f) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}
Chapter 9 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
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