Given the sets, $A=\{0,1\}$ and $B=\{12,1,2\pi\}$, define (by listing the ordered pairs):
$a$) A relation from $A$ to $B$ that is not a function.
$b$) A relation from $A$ to $B$ that is a function.
I was thinking for $b$ that since $A\times B$ is $A$ going to $B$, then I need to write something like:
x y
0 1
12 1
which will give $(0*1) -(12*1)= -12$. But I'm not exactly sure that this is right with the right notation.
On
A relation is a subset of the Cartesian product of the sets. $R\subseteq A{\times} B$. That is, it is a set of ordered pairs whose members are one of the first set, and one of the second (in that order).
$$R = \{(x,y)\in A{\times}B \mid \textsf{some definition}\}$$
$$A{\times}B = \{(1,12), (1, 1), (1, 2\pi), (0, 12), (0, 1), (0, 2\pi)\}$$
So what you are being asked to do is provide examples of such a subset that: (a) is not a function, and (b) is so a function.
This is a test of your knowledge of what is a function, and your practical skills in applying that knowledge.
So, now, back to you: What is a function?
HINT Write down the definition of a relation that is a function. What must be true for a relation not to be a function?