Question

Suppose R_1 and R_2 are partial orders on A. Give either a proof or a counterexample to justify your answer.
Must R_1 U R_2 be a partial order on A?


Please help!

Answer 1

Partial Order-Reflexive,anti-symmetric, and transitive.
Reflexive - the relation is true to itself (a,a)
anti-symmetric- when the relation is only 1 way a->r-->b and b-->r-->a only true when b and a is identical
transitive- a-->r-->b--->r--->c then a--->r--->c

Answer 2

Okay.. Yes.

Answer 3

I basically just let an arbitrary element x be in R_1 and an arbitrary element y be in R_2 and since they're both partial orders, the union would be as well.

Answer 4

dont you have to show how the union of 2 Partial order* relations will also be a partial order though

Answer 5

yeaaa.. but I'm not sure how

Answer 6

tell me if this counter example works

Answer 7

okay

Answer 8

suppose in A
you have an elements that are numbers (1) and element that are colors(Green ball)
your reflexive property property r1 is for all x in A that are same length as themself
your reflexive property r2 can be for all x in A are green

this way you get the color objects in r2 and numbers in r1

Answer 9

but when u combine them it doesnt make sense, the sets are of different type,

Answer 10

this is a weird example, but what u can have is like
A is a set of Reals and integers

Answer 11

No I think I understand..

Answer 12

R_1 reflexive stament can be for all x in A, x is an int
R_2 reflexive statemetn can be for all y in A, y is a nonint

Answer 13

No I think I understand

Answer 14

okok

Answer 15

I have another question if you dont mind.

Answer 16

yeah sure