Math Is Fun Forum

BJNats

Member

Registered: 2008-10-25

Posts: 3

Discrete Mathematics Exam about Binary Relations

Hi!

Will someone help me please?

We just finished our exam in discrete math. Here is the exact problem from our exam (I still don't get how our teacher corrected the exam):

Let S={0,1,2,4,6}. Test the binary relation on S for reflexivity, symmetry, antisymmetry, and transitivity.

p = {(0,0),(1,1),(2,2),(4,4),(6,6),(0,1),(1,2),(2,4),(4,6)}

My answer was:
     Reflexivity: Yes.
     Symmetry: No.
     Antisymmetry: No.
     Transitivity: Yes.

My teacher's answer was:
     Reflexivity: Yes.
     Symmetry: No.
     Antisymmetry: Yes.
     Transitivity: No.

I understand how it is not transitive since (0,1) and (1,2) are related there should be a (0,2) element... and so on...
I just don't understand antisymmetry.

Thanks! I could use any help I can get.

Last edited by BJNats (2008-10-25 19:33:27)

---

No GUTS, no GLORY; No PAIN, no GAIN.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Discrete Mathematics Exam about Binary Relations

The technical definition of antisymmetry says that if A~B and B~A, then A=B.
What this is saying is that if you have two different elements A and B and A~B, then B~A can't happen.

This is true in your case because you have:
- (0,1) but not (1,0)
- (1,2) but not (2,1)
- (2,4) but not (4,2)
- (4,6) but not (6,4)

The first five involve the same element twice, so don't need to be tested for antisymmetry.

---

Why did the vector cross the road?
It wanted to be normal.

BJNats

Member

Registered: 2008-10-25

Posts: 3

Re: Discrete Mathematics Exam about Binary Relations

Wow! Thanks!
I didn't know it was that simple.
I guess I was having a hard time understanding our teacher.
Thanks much!

---

No GUTS, no GLORY; No PAIN, no GAIN.