Question

prove that if A intersection B equals empty set then B intersect A' equals B

Answer 1

WELCOME TO OPENSTUDY!! :D

Answer 2

If there is A' then there has to be a Universal set.
Let
U = {1,2,3,4,5,6}
A = {1,2} [A' = U-A = {3,4,5,6}
B = {4,5,6}

A intersection B = {}
B intersection A' => {4,5,6} intersection {3,4,5,6}
==> {4,5,6} = B :D

Understood? :)

Answer 3

this is just a case, not a proof:(

Answer 4

Yeah?
I don't know any proper proof then. :/

Answer 5

\[assume\space A\cap B=\emptyset\\let\space a\in A^c\cap B\\then\space a\in A^c\space and\space a\in B\\so\space A^c \cap B\subset B\\assume \space b\in B\\since\space A\cap B=\emptyset\\\text{we know that }b\notin A\implies b\in A^c\\so\space b\in A^c \space and\space b\in B\\so\\B\subset A^c\cap B\\so\\B\subset A^c\cap B\space and\space A^C\cap B\subset B\\so\\B=A^c\cap B\]

Answer 6

make sense @arveleyn ?