# Math Help - One to one functions

1. ## One to one functions

I have two sets A,B where B is not the empty set. b is an element of B and a is an element of A.

The function defined by j(a)=(a,b) where (a,b) is an element of AxB.

Show j: A---> AxB for all b in B is one to one.

So I want to show that if j(a1)=j(a2) that implies that a1=a2. I just don't know how to go about proving this. I tried to just assume that j(a1)=j(a2) but I don't think I can just assume that.

Thanks so much for any help!!

2. hmmm
well go ahead and assume that for a1 and a2 in A j(a1) = j(a2).

By the definition of your function
j(a1) = (a1, b1) for some a1 in A and b1 in B and
j(a2) = (a2, b2) for some a2 in A and b2 in B.

Since j(a1) = j(a2) this implies that (a1, b1) = (a2, b2). But this is only true if a1 = a2 and b1 = b2.