[maxreed88]

For any integer n > 1, if Al, A2, A3, ... , An, and B are any sets, then
(A1 -B) (A2 -B) ... (An -B) = (Al A2 A3 … An) -B.

I was able to prove for all sets A, B, and C, (A -B)(C -B)= (AC) - B, and for the above I know that's it's true based on the just mentioned proof but I am having a hard time actually proving it. What steps would I take? I am not looking for an answer just a push in the right direction. Thanks.

maxreed88, on 24 October 2012 - 04:45 PM, said:

For any integer n > 1, if Al, A2, A3, ... , An, and B are any sets, then
(A1 -B ) (A2 -B ) ... (An -B ) = (Al A2 A3 … An) -B.

I was able to prove for all sets A, B, and C, (A -B )(C -B )= (AC) - B, and for the above I know that's it's true based on the just mentioned proof but I am having a hard time actually proving it. What steps would I take? I am not looking for an answer just a push in the right direction. Thanks.

Sorry the emoticon is supposed to be B)

This post has been edited by macosxnerd101: 24 October 2012 - 04:50 PM
Reason for edit:: Disabled emoticons

[macosxnerd101]

This isn't a Game Programming question, so I'm moving this to Computer Science.

Since you don't explicitly specify an operator, I'm assuming you mean the union of these sets? You can use the commutative property to rearrange the ordering of these sets in your set algebra.

[maxreed88]

Thanks, and I figured out some mathematical induction is what I need to use to help prove this.

[maxreed88]

Yes sorry I did not even realize I was missing the union and intersections.

(A1-B)∩(A2-B)∩⋯∩(An-B)=(A1∩A2∩⋯∩A

maxreed88, on 24 October 2012 - 06:03 PM, said:

Yes sorry I did not even realize I was missing the union and intersections.

(A1-B)∩(A2-B)∩⋯∩(An-B)=(A1∩A2∩⋯∩A

This post has been edited by macosxnerd101: 25 October 2012 - 05:39 PM
Reason for edit:: Removed emoticons

[maxreed88]

Solved.