# Prove that if A intersect B = A intersect C then

1. Oct 11, 2012

### Andrax

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

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

2. Relevant equations

3. The attempt at a solution
I have done a lot of work on this exercise nothing seems to work..

2. Oct 11, 2012

### micromass

Staff Emeritus
Can you show us the work you did?

3. Oct 11, 2012

### 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 im stuck here.. i need to prove that x E A and x E/ B = x E A and x E/ C...