So A ∪ B = A + B − A ∩ B

A ∪ B ∪ C = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)

So i see where this is going...

Now to prove by induction how would i start?

Printable View

- Oct 15th 2011, 04:57 PMAquameatwadAnother Proof by Induction
So A ∪ B = A + B − A ∩ B

A ∪ B ∪ C = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)

So i see where this is going...

Now to prove by induction how would i start? - Oct 15th 2011, 06:26 PMDevenoRe: Another Proof by Induction
start by assigning a natural number to something. i suggest calling your sets $\displaystyle \{A_j : j\in \{1,2,\dots, k\}\}$ and using induction on k.

that is, you are doing induction on "the number of sets you are taking the union of". your base case is k = 2, although you have also listed k=3.

one hopes you have previously established that (A U B) U C = A U (B U C), so that A U B U C is unambiguous.