define ~ on Z by a~b iff 3a+b is a mulitple of 4.
so far i only have reflexive...
how can i prove that its symmetric and transitive?
First it's symmetric if .
Now means that is a multiple of . And if we're going to show that , we shall need to show that this will mean that is also multiple of . So, read carefully through Chris L T521's answer. He has clearly shown that if is a multiple of then is also a multiple of .
Then, what does it mean to prove that is transitive? It is this: if and , then we must prove that . Translating this into multiples of , this is: if is a multiple of , and is a multiple of , then we must prove that is also a multiple of . Chris L T521's answer has shown you how to build up an expression for starting with and . Study it again, and make sure that you can see how this shows that is a multiple of .