There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0, 1), (1, 1)} (b) {(0, 0)} (e) {(1, 1)} (h) {(0, 0), (1, 1)} (k) {(1, 0), (1, 1)} (n) {(0,0), (1, 0), (1, 1)} (c) {(0, 1)} (f) {(0, 0), (0, 1)} (i) {(0, 1), (1,0)} (I) {(0,0), (0, 1), (1, 0)} (0) {(0,1), (1, 0), (1, 1)} (m) {(0,0), (0, 1), (1, 1)} (p) {(0, 0), (0, 1), (1, 0), (1, 1)} For a-f use the letters for each relation above. a. List the reflexive relations on the set {0, 1}. b. List the irreflexive relations on the set {0, 1}. c. List the symmetric relations on the set {0, 1}. d. List the transitive relations on the set {0, 1}. e. List the antisymmetric relations on the set {0, 1}. f. List the asymmetric relations on the set {0, 1}.
There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0, 1), (1, 1)} (b) {(0, 0)} (e) {(1, 1)} (h) {(0, 0), (1, 1)} (k) {(1, 0), (1, 1)} (n) {(0,0), (1, 0), (1, 1)} (c) {(0, 1)} (f) {(0, 0), (0, 1)} (i) {(0, 1), (1,0)} (I) {(0,0), (0, 1), (1, 0)} (0) {(0,1), (1, 0), (1, 1)} (m) {(0,0), (0, 1), (1, 1)} (p) {(0, 0), (0, 1), (1, 0), (1, 1)} For a-f use the letters for each relation above. a. List the reflexive relations on the set {0, 1}. b. List the irreflexive relations on the set {0, 1}. c. List the symmetric relations on the set {0, 1}. d. List the transitive relations on the set {0, 1}. e. List the antisymmetric relations on the set {0, 1}. f. List the asymmetric relations on the set {0, 1}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:There are 16 binary relations on the set {0, 1}:
(a) { }
(d) {(1,0)}
(g) {(0, 0), (1, 0)}
(j) {(0, 1), (1, 1)}
(m) {(0,0), (0, 1), (1, 1)}
(b) {(0, 0)}
(e) {(1, 1)}
(h) {(0, 0), (1, 1)}
(k) {(1, 0), (1, 1)}
(c) {(0, 1)}
(f) {(0, 0), (0, 1)}
(i) {(0, 1), (1,0)}
(1) {(0,0), (0, 1), (1, 0)}
(0) {(0, 1), (1, 0), (1, 1)}
(n) {(0,0), (1,0), (1, 1)}
(p) {(0, 0), (0, 1), (1, 0), (1, 1)}
For a-f use the letters for each relation above.
a. List the reflexive relations on the set {0, 1}.
b. List the irreflexive relations on the set {0, 1}.
c. List the symmetric relations on the set {0, 1}.
d. List the transitive relations on the set {0, 1}.
e. List the antisymmetric relations on the set {0, 1}.
f. List the asymmetric relations on the set {0, 1}.
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