# Proof by induction A u B = A + B - A n B

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• Oct 19th 2011, 06:58 PM
Aquameatwad
Proof by induction A u B = A + B - A n B
So for the union of A1 and A2 .. A1 u A2 = A1 + A2 - A1 n A2

Prove by induction that it is true for all Unions

So i start with another Union A3 so,

A1 u A2 u A3 = A1 + A2 +A3 - (A1 n A2) - (A1 n A3) - (A2 n A3) + (A1 n A2 n A3)

now i want to to prove for n+1. or for all unions

How would i do this?
• Oct 19th 2011, 07:01 PM
Prove It
Re: Proof by induction A u B = A + B - A n B
Quote:

Originally Posted by Aquameatwad
So for the union of A1 and A2 .. A1 u A2 = A1 + A2 - A1 n A2

Prove by induction that it is true for all Unions

So i start with another Union A3 so,

A1 u A2 u A3 = A1 + A2 +A3 - (A1 n A2) - (A1 n A3) - (A2 n A3) + (A1 n A2 n A3)

now i want to to prove for n+1. or for all unions

How would i do this?

Start by at least setting up an equation for $\displaystyle A_1 \cup A_2 \cup A_3 \cup \dots \cup A_n$ that you want to prove...
• Oct 19th 2011, 07:19 PM
Aquameatwad
Re: Proof by induction A u B = A + B - A n B
So,

(UAi) = ∑Ai - ∑(Ai n Aj) + ∑(Ai n Aj n Ak ) + ... +∑(Ai n Aj ... Aq) - ∑(A1 n A2 .... n An)

is this correct?