Thread: help on discrete math,please?:-)

here's the question and has to do with order and symbol series:
let A be the set of all bit symbol series of the size of 11. Let also R be a relation on A where 2 symbol series are connected iff the 3 first bits are the same.sHOW that R is reflexive, antisymmetric, and transitive....i hope MY translation from greek to english is not TOO bad...
thanks in advance
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...

Originally Posted by aegean

let A be the set of all bit symbol series of the size of 11. Let also R be a relation on A where 2 symbol series are connected iff the 3 first bits are the same.sHOW that R is reflexive, antisymmetric, and transitive....i hope MY translation from greek to english is not TOO bad...

You translation is good.
Here are a few suggestions for your translation: “all bit symbol series” = “bit-strings”
“connected” = “related”.

There is a mistake. The word “antisymmetric” must surely be “symmetric”.
As described the relation is an equivalence relation; it is reflexive, symmetric, and transitive.
Any time we have a “same as” relation that is true.
If a=10100001000 & b=10111111111 then clearly aRb & bRa but a is not equal to b.
Therefore the relation is not antisymmetric.