Hello...

I gotta a couple of questions regarding graph theory I hope you guys can help me with.

Q1- Let R be a symmetric relation defind on a set C. Prove or disprove that R^5 is a symmetric relation.

Q2- Suppose that R is a relation defined on a set A that is not reflexive. Prove or disprove that R^3 is not reflexive.

Q3- Let A be the of all bit strings of length 25. Ler R be the relation define on A where two bit strings are related in the first 3 bits are the same.

a- Show that R is an equivalence relation.

b- Enumerate one bit string from each of the fifferent equivalence relation classes on R.

Any help would be appreciated. Thanks in advance.