Question

91 Uy UdU YZ SU
(cy) (y) > 0
+ 2y2x > 0
x2 > 0
(y2 > 0)
Rz
Hence R is transitive. Note that, (2)(3) >0 = 2R3 and (3)(2) >0 = 3R2
So, 2R3 and 3R2 but 2 +3. Hence R is not antisymmetric. Hence R is not partial order relation.
Exercise:2.1
1. Let A{1,2,3,4}. For each of the relation defined below, determine whether R is reflex
symmetric or transitive.
(a) R={(1,1),(1,2), (2,1), (2, 2), (3, 3), (3,4),(4,3), (4,4)}
(b) R= {(1,1), (2, 2), (3,3)}​

Answer 1

Answer:

91 Uy UdU YZ SU

(cy) (y) > 0

+ 2y2x > 0

x2 > 0

(y2 > 0)

Rz

Hence R is transitive. Note that, (2)(3) >0 = 2R3 and (3)(2) >0 = 3R2

So, 2R3 and 3R2 but 2 +3. Hence R is not antisymmetric. Hence R is not partial order relation.

Exercise:2.1

1. Let A{1,2,3,4}. For each of the relation defined below, determine whether R is reflex

symmetric or transitive.

(a) R={(1,1),(1,2), (2,1), (2, 2), (3, 3), (3,4),(4,3), (4,4)}

(b) R= {(1,1), (2, 2), (3,3)}