[mojo666]

eZACKe, on 03 February 2011 - 04:41 PM, said:

Thank you.

I need some practice.

First, it seems you don't understand the definitions. It is important to understand what all these operations mean before you try to prove something.

Union: L3 = L1∪L2
L3 is all elements of L1 and L2
It is not everything that is not mutual. Mutuals are included.

Reverse: L2 = L1R
L2 is every element of L1 reversed.
It is not every element listed in reverse order.
For example it seems you thought that {1,2,3,4,5,6}R = {6,5,4,3,2,1}. This is not what reverse does. {1,2,3,4,5,6}R = {1,2,3,4,5,6}. The following is an example of how Reverse works: {11,12,13,14,15,16}R = {11,21,31,41,51,61}. It's not the order of elements in the set that changes, it's the elements themselves that change.

Once you understand that, I think it is helpful to try and find the solution in common terms before any attempt at formal reasoning. The problem asks if combining two languages then reversing their strings is the same as reversing the strings first then combining the results. The answer is obviously yes. Reversing a set of strings produces the same results regardless if you throw them in a pile before or after the reversal. Now express this to formal reasoning and you have your proof.