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**1. The problem statement, all variables and given/known data**

Prove that if A_1,A_2,…,A_n and B are sets, then

(A_1 – B) U (A_2 – B) U … U (A_n – B) = (A_1 U A_2 U … U A_n) – B.

**2. Relevant equations**

The chapter this is in is based on mathematical induction, which might be a big hint.

Mathematical induction:

Step 1: Prove for the base-case (n = 1)

Step 2: Prove for the general case (n = k)

Step 3: Prove for the advancing case (n = k+1)

**3. The attempt at a solution**

I haven't a clue how to prove this in mathematical terms, but I know how to give an analogy to demonstrate that I understand the scenario.

Imagine people are lined up to enter a building. As they enter the building (As you introduce each union), each person is carrying a bag (A1, A2, A3, etc). When they enter the building, their bags are searched, and anything on the "No-entry" list (Set B) is removed (An airport example would be removing sharp objects, etc).

(Left side:) If you let people in, and remove their "No-entry" objects upon entry...

(equals)...the result will be the same as...

(Right side:) ...if you let them all in, and then removed their "No-entry" objects inside.

This demonstrates that I understand the problem, and through just gosh darned common freakin' sense, I know that this is a true fact.

However, I predict only getting part marks for not using mathematical induction, OR for not using mathematical terms.

My car has stalled; can anyone gimme a push? ;)

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