Can someone help me with this proof please.
Let n be a positive integer. If A1, A2, ... , An are pairwise disjoint finite sets then | A1 U A2 U ... U An| = |A1| + |A2| + ... + |An|.
Yeah sure. So we proved about the base case when you adjoin 1 disjoint set to A that is how you count them.
So suppose for induction hypothesis that for disjoint sets we have , we now show it must be true for adjoining n+1 disjoint sets. So are all disjoint. By induction hypothesis . Now we notice so by our base case in the first post
Which completes the induction.