1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Prove that if A intersect B = A intersect C then

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that if A [itex]\cap[/itex] B = A [itex]\cap[/itex] C [itex]\Leftrightarrow[/itex] A [itex]\cap[/itex] [itex]\neg[/itex]B = A [itex]\cap[/itex] [itex]\neg[/itex]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. jcsd
  3. Oct 11, 2012 #2
    Can you show us the work you did?
  4. Oct 11, 2012 #3
    All i pretty much did so far was turning the A [itex]\cap[/itex] LB = A [itex]\cap[/itex] C [itex]\Leftrightarrow[/itex] A - B = A - C
    i've tried pretty much everything nothing seems to work
    example : let x E a ---> x E A [itex]\cap[/itex] B ---> x E A [itex]\cap[/itex] C
    yeah i'm pretty much stuck here
    also i tried this one A [itex]\cap[/itex] B = A [itex]\cap[/itex] C [itex]\longrightarrow[/itex] x E A and x E B and x E C [itex]\Longrightarrow[/itex] 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...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook