Test by Bikram | Mathematics | Test 2 | Question: 22

Question

   Which one of the following is a Partial Order Relation ?

1. 
2. 
3. 

Refer the Partial Order Diagram above.

• A. b and c
• B. a and b
• C. a and c
• D. c only

Answer 1

For a relation to be a partial order relation it must be Reflexive, Anti symmetric and Transitive.
For a relation to be transitive it must follow transitive property.
Transitive property: If a R b and b R c then a R c. Where a R b means a is related to b.

In A graph, a R b and b R d but a is not related to d. It is violating the transitive property. Hence it is not Partial order relation.
In B graph, c R d and d R b but c is not related to b. It also violated the transitive property.
For C graph,
As every vertex has Self loop,  indicating that graph is reflexive.
It is anti symmetric because whenever a R b and b R c imples (a = b).
It is transitive also. because there is no case where x R y and y R z. So x R y and y R z become false. Whenever in P $\rightarrow$ Q , P become false,  P $\rightarrow$ Q become True.
So C graph is Partial order relation. 

Ans: D.

Comments

good observation :)

Answer 2

A: Transitivity is violated.

B: Transitivity is violated.

C: Reflexive, anti-symmetric, transitive. (self-loops, arrowheads flowing in just one direction, and transitivity isn't violated).

Hence, Option D