5 Let n N Prove modulo n is a transitive relationSolutionle

5. Let n N. Prove “” modulo n is a transitive relation

Solution

let a=b modulo n,

b = c modulon

=>

n |(a-b),

n |(b-c)

=>

n|(a-b)+(b-c)

=>

n |(a-c)

=>

a = c mod n

=>

“” modulo n is a transitive relation

thus proved