let R be a reflexive and symmetric relation on a set X. let's define a relation S on X. by (x,y) in S iff there exists a finite sequence x0,x1,...,x_n(adsbygoogle = window.adsbygoogle || []).push({});

of terms from X such that x0=x xn=y and (x_i,x_i+1) in R for i=0,1,...n-1.

now ive proven that S is an equivalence relation, i need to show that S is the smallest equivalence relation that includes R, i.e if R is a subset of T then S is a subset of T.

i think that the naswer is simple but perhaps too simple to be true.

if (x,y) in S, then there exists a finite sequence x,y such that (x,y) in R and so (x,y) in T.

am i right here?

thanks in advance.

i hope you can answer also my other threads which i have opened here, cause im having an exam in friday in this material and your help is understandably important for me.

**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!

# Question on equivalence relation.

Can you offer guidance or do you also need help?

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