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Matrix relation of sets. symmetric, antisymmetric,reflexive,transitive 
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#1
May508, 07:38 PM

P: 120

1. The problem statement, all variables and given/known data
relation A = {a,b,c} for the following matrix [1,0,0;1,1,0;0,1,1] is it reflexive, transitive, symmetric, antisymmetric 2. Relevant equations ordered pairs. 3. The attempt at a solution i wrote the ordered pairs as (a,a),(b,a),(b,b),(c,b),(c,c) I only that it is reflexive for a,a b,b and c,c also it is antisymmetric because there are no edges in opposite directions between distinct verticies. am I missing anything. thanks! 


#2
May608, 05:15 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,564

To be symmetric, since it contains (b,a) it would have to contain (a,b) and it doesn't: not symmetric. Since it does NOT contain (a,b) or (b,c), yes, it is antisymmetric. What about transitive? A relation is transitive if and only if, whenever (x,y) and (y,z) are in the relation, so is (x,z). Can you find pairs so that is NOT true? 


#3
May608, 02:02 PM

P: 120

Hey, thanks for the reply!
I didn't put parenthesis around the ordered pairs (a,a),(b,b),(c,c) for the first problem, sorry. I don't think it's transitive since we have (c,b) and (b,a), and it doesn't contain (c,a). How does that sound? Thanks 


#4
May608, 02:22 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,564

Matrix relation of sets. symmetric, antisymmetric,reflexive,transitive
Yes, that completes it.



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