Relations handout

Relations handout - | = | y |} . Is this relation reexive?...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 100 Relations Handout Martin H. Weissman The following are relations on the set S = { a,b,c } : The first relation is: R = { ( a,b ) , ( b,c ) , ( c,a ) , ( b,a ) , ( c,b ) , ( c,a ) } . Is this relation reflexive? symmetric? transitive? antisymmetric? If your answer to any of the above questions is “no”, then provide a counterexample. For example, the relation is not reflexive, since ( a,a ) 6∈ R . The second relation is: R = { ( a,a ) , ( a,b ) , ( a,c ) , ( b,b ) , ( b,c ) , ( c,c ) } . Is this relation reflexive? symmetric? transitive? antisymmetric? Provide counterexamples if your answers are “no”. Is this an equivalence relation? A partial order? The third relation is a relation on R : R = { ( x,y ) R 2 such that | x
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: | = | y |} . Is this relation reexive? symmetric? transitive? antisymmetric? Is it an equivalence relation? a partial order? The fourth relation is a relation on S again: R = { ( a,a ) , ( a,b ) , ( b,a ) , ( b,b ) , ( c,c ) } . Is this relation reexive? symmetric? transitive? antisymmetric? Is it an equivalence relation? a partial order? The fth relation is a relation on Z : R = { ( x,y ) Z 2 such that x-y 1 } . Is this relation reexive? symmetric? transitive? antisymmetric? Is it an equivalence relation? a partial order? 1...
View Full Document

This note was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.

Ask a homework question - tutors are online