## why is this equal to the empty set

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

### why is this equal to the empty set

Hi, I am trying to understand why the line with the **** is equal to the empty set.

Let U be the set of positive integers and

A = {1,2,3,4,5,6}, B = {2,4,6} and C = {1,3,5}

Then, A - (B intersection C) = A - (empty set) = A

and

(A - B) intersection (A - C) = (1,3,5) intersection {2,4,6} = (empty set) <=== Why is this equal to the empty set?

Thus, A - (B intersection C) not= (A - B) intersection (A - C)

Thanks for any help.
tonyc1970

Posts: 17
Joined: Fri Aug 02, 2013 4:58 pm

### Re: why is this equal to the empty set

tonyc1970 wrote:...(1,3,5) intersection {2,4,6} = (empty set) <=== Why is this equal to the empty set?

What element do you believe should be contained within the intersection, such that said intersection should not be empty? Kindly please provide your reasoning in addition to your answer. Thank you.
nona.m.nona

Posts: 256
Joined: Sun Dec 14, 2008 11:07 pm