Hi i need help with this following question. I am not sure on how to approach it.
Define the relation R on by is divisible by 7
Prove that R is an equivalence relation on and describe the equivalence classes and
Any help is appreichated
thanks
how did you calculate the equivalence classes because i know that some being mod 7 means it divisble by some multiple of 7 and remainder is written in the front of the mod7. hence 34=6mod7 since 34-(7x4)=6.
but i don't understand how you've done it in terms of x and y. and also could you please explain the sqaure bracket notation for the equivalence classes. I have seen this notation before but i don't understand what the number inside the brackets and the lower case power to it means.
thanks for your help
Sure thing. You may wish to memorize this extremely useful theorem:
For any two integers , an integer divides if and only if .
So, if divides , then . Similarly, if divides , then . And so if divides either or , then .
As for the notation issue, for some integers and , we have the equivalence class (the set of integers which, when divided by , have a remainder of ).