Yes, its suppose to be there - that is the basic idea of the equation (of the sets union) - adding the ‘next set’ does not take into consideration the elements of the first one and the ‘previous’ does not take into consideration the elements of the actual set.
What I meant is that for the...
The problem is that I don’t have any idea how to use the ‘induction hypothesis’.
(I can use it If I add the set An+1 to the left side of the equation, but this leads me to nothing).
The hypothesis somehow should be used (I guess) to the right side of the equation (using set algebra properties...
I hope that someone can help me with the following problem:
Problem: Proof by induction that:
A1 \cup A2 \cup...\cupAn=(A1-A2)\cup(A2-A3)\cup...\cup(An-1-An)\cup(An-A1)\cup
(A1\capA2\cap...\capAn)