# Thread: i do need some help....

1. ## i do need some help....

here's the question and has to do with order and string-series:
let A be the set of all bit string-series of the size of 11. Let also R be a relation on A where 2 string-series are related iff the 3 first bits are the same.sHOW that R is reflexive,symmetric, and transitive....i hope MY translation from greek to english is not TOO bad...
ps:actually the symbol series will be 8...
we are interested in only about the 3 first bits
000.....
001.....
010....
011....
100....
101....
110...
111...
we intuitively understand that is reflexive...how we prove...and what aboutsymmetric & transitive....?

2. Originally Posted by aegean
we intuitively understand that is reflexive...how we prove...and what aboutsymmetric & transitive....?
As I said before, anytime you has the relation defined as “same as” it is easily shown to be an equivalence relation.
If a has the same first three bits as b then b has the first three bits as a: symmetric.

If a has the same first three bits as b and b has the same first three bits as c, then clearly a has the same first three bits as c: transitive.