Question

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.

Answer 1

Prove.

Answer 2

I was able to prove for all sets A, B, and C, (A -B)(C -B)= (AC) - B, and that should help me solve this but I am still having trouble.

Answer 3

you can take insquality in use

Answer 4

is it supposed to be like this
\[ \large (A_1\setminus B)\cap(A_2\setminus B)\cap\dots\cap
(A_n\setminus B)=(A_1\cap A_2\cap\dots\cap A_n)\setminus B \]
?

Answer 5

Yes I am so sorry I did not even realize that the unions and intersections were missing

Answer 6

well intersections only anyways

Answer 7

this is very easy. just use the definition
\[ \large K\setminus M=K\cap M^c \]
the associative property of iintersection and this one
\[ \large K\cap K=K \]

Answer 8

Thank you I see now, that is what I needed to give me the push in the right direction now I can prove it much more easily.