1. Originally Posted by MoeBlee
For each f in {f | f is a function from BuC into A} you're going to choose an appropriate g and h where <g h> is in
{g | g is a function from B into A} X {h | h is a function from C into A}.

Now, think about f. It's a function whose domain is BuC. But B and C are disjoint. So f is the union of two functions, one function from B into A and another function other from C into A.

So, for a given f, what should g and h be?
g should be the function the takes B into A.

h should be the function the takes C into A.

If that's right then I truly do not understand this course.

Edit... I dunno...

2. Look Moe can you just write down the actual bijection and ill show you what part of it I don't understand. Swear to jebus we'll be here forever if you want me to discover it myself.

3. I've as much as given it to you.

To finish it off, first I'll introduce a notation:

Let 'r' stand for restriction. I.e., for sets X and Y, we have

XrY = {<p q> | <p q> in X and q in Y}.

In other words, XrY is the set of all the ordered pairs <p q> in X such that p is in Y.

Each f in {f | f is a function from BuC into A} is of this form:

frB u frC.

That's just another way of saying what I mentioned in my last post.

So for f in {f | f is a function from BuC into A} let's map f to
<frB frC>.

So let J be this mapping:

For f in {f | f is a function from BuC into A},
let J(f) = <frB frC>.

In other words, for f in {f | f is a function from BuC into A}, I'm mapping f to some g and some h such that
<g h> is in
{g | g is a function from B into A} X {h | h is a function from C into A}, and
g and h are specifically frB and frC.

Now, all that remains is to prove that this J as just defined IS a bijection from {f | f is a function from BuC into A} onto
{g | g is a function from B into A} X {h | h is a function from C into A}.

So, I'd like you now to do that.

4. So I guess you figured out the proof that J is a bijection.

5. Originally Posted by MoeBlee
So I guess you figured out the proof that J is a bijection.
No. This is taking too much of my time up. The proofs not as basic as I thought if would be and I have waaaay too much other stuff to be doing. 9 exams and this probably wont show up on the one exam it could be in. Not worth the time. I thank you for your effort.