Page 29 - Discrete Structure II

M1 = { 1, 2, 3, 4, 5, 6, …}

M2 = ( 2, 4, 6, 8, 10, ….

CM1M2 = { 2, 4, 6, ……

Exercises

1) List all ordered pairs in the relation R = {(a,b) | a divides b} on the set {1,2,3,4,5,6}

2) For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, symmetric,
antisymmetric or transitive

a) R = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4) }
b) R = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4) }
c) R = { (2,4), (4,2)}
d) R = {(1,2), (2,3), (3,4) }
e) R = {(1,1), (2,2), (3,3), (4,4) }
f) R = {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4) }

Solution

1) List all ordered pairs in the relation R = {(a,b) | a divides b} on the set {1,2,3,4,5,6}

R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), (6, 6)}

1) For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, symmetric,
antisymmetric or transitive

a) R = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4) }

Reflexive No (1,1)  R
Symmetric No (2,4)  R and (4,2)  R
Antisymmetric No (3,2) , (2, 3)  R and 2  3
Transitive Yes