Sets help interpreting question

[DorumonSg]

I have this question but I don't get it at all. Here goes:

Let X be {x, y, z}
P(X) is the power set.
For all Y,Z is an element of P(X), Y R Z where The number of elements in Y intersect Z is 1.

So I worked out P(X) to be:

{(null), (x), (y), (z), (x,y), (x,z), (y,z)}

Then I don't get the next line, how can the number of elements of Y intersect Z be 1 if all members of Y and Z are elements of P(X)? Isn't Y = Z?

 

[tiny-tim]

Hi DorumonSg!

(you missed out (x,y,z) )

For example, (x,y) R (x,z) and (x,y) R (x) but not (x,y) R (z) and not (x,y) R (x,y,z).

 

[DorumonSg]

So Y R Z is supposed to be:

{((x),(x,y)), ((x),(x,z)), ((x),(x,y,z)), ((y),(x,y)), ((y),(y,z)), ((y),(x,y,z)), ((z),(x,z)), ((z),(y,z)), ((z),(x,y,z)), ((x,y),(x,z)), ((x,y),(y,z)), ((x,z),(y,z))}

You mean like that?

 

[tiny-tim]

Yup!

 

[DorumonSg]

Thanks alot.

Am I also right to say that Y R Z is not Reflective, Symmetric, Anti-Symmetric, Transitive, Partial Order and Total Order?

 

[tiny-tim]

Am I also right to say that Y R Z is not Reflective, Symmetric, Anti-Symmetric, Transitive, Partial Order and Total Order?

No..

 

[DorumonSg]

Eh? But I don't see any relations between them.