Am I Getting the Hang of Relations

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In summary, the relation R on the set of real numbers is defined by xRy if (x < 0) or (x >= 0 and x = y). It is reflexive because for any x, x is always equal to itself. It is symmetric because if a positive y is chosen, it is symmetric due to the conditions of the relation, and the same applies for a negative y. It is also transitive because if xRy and yRz, then either x < 0 and xRz, or x >= 0 and x = y so xRz due to yRz.
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Learning_Math
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1. R on the set (the reals) defined by xRy iff (x < 0) or (x > or equal to 0 and x = y)



2. None



3.

Reflexive - Yes, since no matter what x I choose, x will always be equal to x, and will therefore fit the conditions of the relation.

Symmetric - It is symmetric because if I choose a positive y, then it is symmetric because of (x > or equal to 0 and x = y). If I choose a negative y, it is symmetric because of (x < 0).

Transitive - I am a little unclear on this one. I think however, that it is transitive because if I choose a positive z, then it is transitive because of (y > or equal to 0 and y = z). If I choose a negative z, it is transitive because of (y < 0).
 
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  • #2
I don't think it's symmetric. For example, it seems xRy but not yRx when x=-1 and y=1.

And I think you're right that it is transitive. However, it seems like you'd want to condition on x rather than z. That is, suppose xRy and yRz.
Then either x<0, in which case xRz. Or x>=0, in which case x=y so xRz because yRz.
 
  • #3
That was helpful, thank you grief.
 

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