<Moderator's note: Moved from a technical forum and thus no template. Also re-edited: Please use ## instead of $$.>(adsbygoogle = window.adsbygoogle || []).push({});

If ##R_{1}## and ##R_{2}## are relations on a set S with ##R_{1};R_{2}=I=R_{2};R_{1}##. Then ##R_{1}## and ##R_{2}## are bijective maps

##R_{1};R_{2}## is a composition of two relations

For the surjectivity part, I showed that if ##(a,b)\in I## then ##(a,c)\in R_{1}## and ##(c,b)\in R_{1}## and ##(a,c)\in R_{2}## and ##(c,b)\in R_{2}## for some ##c\in S##. Now for arbituary ##(x,y)\in R_{1}## we have ##(x,z)\in I## which implies that ##(y,z)\in R_{2}##. But also ##(y,z)\in R_{1}##, so ##R_{1}## is surjective. Similar argument for ##R_{2}##

And for Injectivity, I've tried to show that if ##aR_{1};R_{2}c## and ##bR_{2};R_{1}c##, then ##a=b## but I am not entirely sure what ##a=b## means in this context.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

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!

# Homework Help: How can I prove that these relations are bijective maps?

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**