define ~ on Z by a~b iff 3a+b is a mulitple of 4.
so far i only have reflexive...
reflexive: 3a+a=4a
how can i prove that its symmetric and transitive?
Hello glopez09You need to work out what it is you need to prove, in order to show that is 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 .
Grandad