Relation Equation Graphs/Ordered Pairs

[johnny101]

Hello!

I have to write the following relations as a set of ordered pairs, and I'm somewhat confused by the simplicity of it(go figure). Rather than a relation like the other examples with arrows from the points(a to b, a to c, a to d, etc), its just two points 1 and 2. Not connected by anything or any arrows to themselves. Just dots. Are the points(1,1)(2,2)? Wouldn't that require a loop?

 

[daon2]

Hello!

I have to write the following relations as a set of ordered pairs, and I'm somewhat confused by the simplicity of it(go figure). Rather than a relation like the other examples with arrows from the points(a to b, a to c, a to d, etc), its just two points 1 and 2. Not connected by anything or any arrows to themselves. Just dots. Are the points(1,1)(2,2)? Wouldn't that require a loop?

Empty set?

 

[johnny101]

The book had a prior example of a diagram for (a,b,c) with data, and A was a loop, B was a loop, and C was just a dot but it was labeled (a,b,c). Which is why I was going towards just labeling it (1,2) if 1 and 2 are just dots??

 

[daon2]

The book had a prior example of a diagram for (a,b,c) with data, and A was a loop, B was a loop, and C was just a dot but it was labeled (a,b,c). Which is why I was going towards just labeling it (1,2) if 1 and 2 are just dots??

Then I have no idea what is being asked of you. I was thinking that a directed edge from a to b would mean (a,b) belongs to the relation

 

[johnny101]

I was just asking for clarification that if given the relation points in a graph of simply 2 dots displaying a 1 coordinate and 2, is that labeled as (1,2) or (1,1)(2,2)?

 

[daon2]

I was just asking for clarification that if given the relation points in a graph of simply 2 dots displaying a 1 coordinate and 2, is that labeled as (1,2) or (1,1)(2,2)?

Again, my answer, without having your notes, would be the empty set as there are no edges. Directed graphs and binary relations are the same thing in my mind.

For example, in the below image the induced binary relation is: {(1,2),(2,3),(3,1),(2,5),(4,5),(5,5)}.