Prove that if A intersect B = A intersect C then

[Andrax]

Homework Statement

Prove that if A $\cap$ B = A $\cap$ C $\Leftrightarrow$ A $\cap$ $\neg$B = A $\cap$ $\neg$C

Homework Equations

The Attempt at a Solution

I have done a lot of work on this exercise nothing seems to work..

 

[micromass]

I have done a lot of work on this exercise nothing seems to work..

Can you show us the work you did?

 

[Andrax]

All i pretty much did so far was turning the A $\cap$ LB = A $\cap$ C $\Leftrightarrow$ A - B = A - C
i've tried pretty much everything nothing seems to work
example : let x E a ---> x E A $\cap$ B ---> x E A $\cap$ C
yeah I'm pretty much stuck here
also i tried this one A $\cap$ B = A $\cap$ C $\longrightarrow$ x E A and x E B and x E C $\Longrightarrow$ x E A and x E l B and x E l C And I am stuck here.. i need to prove that x E A and x E/ B = x E A and x E/ C...