lec1019 - Problems involving relation composition Prove or...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Problems involving relation composition Prove or disprove: If a relation R, defined as a subset of A x A, is symmetric, then show that R ° R is symmetric as well. Since R is symmetric, we know that if (a,b) R, then (b,a) R. We must prove under this assumption that if (a,b) R ° R, then (b,a) R ° R. If (a,b) R ° R, by the definition of function composition, we must have an element c A such that (a,c) R and (c,b) R. But we know R is symmetric. Thus, we can deduce that (c,a) R and (b,c) R. But, if this is the case, by the definition of function composition, we must have (b,a) R ° R, because (b,c) R and (c,a) R. This is exactly what we needed to prove. Thus, R ° R is symmetric. Prove: R is transitive R R R. We must show that if (a,b) R ° R, then (a,b) R. First of all, if (a,b) R ° R, then by the definition of function composition, there exists an element c of A such that (a,c) R and (c,b) R. But, we also know that R is transitive. Since we have (a,c)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 06/09/2011.

Page1 / 4

lec1019 - Problems involving relation composition Prove or...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online