# Math Help - inclusion exclusion principle help!

1. ## inclusion exclusion principle help!

if A,B and C are finite sets with the following properties:
B has 2 more elements than A;C is twice as big as B;
AnB is the same size as AnC;B and C have no elements in common.
prove that |AnBnC| is divisible by 2 (i.e. has an even number of elements)

2. ## Re: inclusion exclusion principle help!

Originally Posted by university
if A,B and C are finite sets with the following properties:
B has 2 more elements than A;C is twice as big as B;
AnB is the same size as AnC;B and C have no elements in common.
prove that |AnBnC| is divisible by 2 (i.e. has an even number of elements)
Because "B and C have no elements in common", $|A\cap B \cap C|=0$.
Zero is an even number.