# Binary Relations

• Oct 8th 2009, 02:00 PM
GreenDay14
Binary Relations
I have a question here that states:

With a table like that in Fig. 2.2, illustrate a relation on the set {a,b,c,d} that is:

i) not symmetric and not antisymmetric
and ii) transitive

(the table in question is your basic 5x5 table which abcd in both the x and y axis, and the corresponding relations are checked off in the boxes)

I thought about it and resulted in:

i) {(a,a), (b,b), (c,b), (c,c)} --> does this make sense?

and for ii) could i just put: {(a,a), (b,b), (c,c), (d,d)}?

Any help would be greatly appreciated. Thanks.
• Oct 8th 2009, 03:10 PM
Plato
Quote:

Originally Posted by GreenDay14
illustrate a relation on the set {a,b,c,d} that is:
i) not symmetric and not antisymmetric
and ii) transitive
I thought about it and resulted in:

i) {(a,a), (b,b), (c,b), (c,c)} --> does this make sense?

That is not symmetric. Did you mean (b,c)?
• Oct 8th 2009, 03:24 PM
GreenDay14
Yes I did sorry. I think I arrived at the right answer for that one. It's the second one that is really confusing me.
• Oct 8th 2009, 04:11 PM
Plato
The diagonal of any set, $\Delta_A$, is an equivalence relation.