Hey everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I'm working through the first chapter of Mendelson's Topology right now and ran into this question:

Let P be a subset of real numbers R such that i) 1 is in P, 2) if a,b are in P then a+b are in P, and 3) for each x in R, either x is in P, x=0, or -x is in P. Define Q= {(a,b) such that (a,b) is in R x R and a-b is in P}. Prove that Q is transitive.

The only reason I'm unsure about this is because my proof was very short and didn't involve 2 of the properties. This is what i said:

To prove Q is transitive, we prove that if aRb and bRc then aRc. Suppose aRb and bRc, then by definition of Q a-b is in P and b-c is in P (and hence in Q). According to property 2 then, (a-b)+(b-c) is in P, or a-c is in P and hence Q, so Q is transitive.

See why I'm confused? Did I miss something?

Thanks for your help.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on Relations

Loading...

Similar Threads for Question Relations | Date |
---|---|

A question related to an exponential random variable | Nov 14, 2011 |

Question related to IID process | Nov 2, 2011 |

Question on reflexivity, symmetry, and transitivity (Relation on X (Attempt inside)? | Nov 1, 2011 |

More questions about Relations | May 8, 2011 |

Question about relations | May 6, 2011 |

**Physics Forums - The Fusion of Science and Community**