How about this:

Let R = A1

S = A2

For each (a1, a2) e (A1 * A2), for which P1(a1), P2(a1, a2), we have:

{ xi e Ai | Pi(a1, a2) } = {xi e Ai | xi e Ai} = Ai

where i=1,2

therefore mi = | {xi e Ai | Pi(a1, a2)} |

for i=1,2 (mi denotes size of set Ai)

Therefore:

C = { (a1, a2) e (Product,j=1 to 2) (Aj | P1(a1), P2(a1, a2) }

= { (a1, a2) e (Product,j=1 to 2) (Aj | a1 e A1, a2 e A2) }

= A1 * A2

Hope that makes sense. P() means power set.

i can’t get my head around this…

the cartesian product of two sets is defined as RxS = { (x,y) | x e R, y e S }

i now need to proof that :

obviously this is true. but i am clueless as to how a proper way to express it in a mathematical proof would look like. if anybody could help me i’d be very glad. thanks guys.