N is the number of ordered pairs of non-empty sets P and Q that have the following properties:

1. P ⋃ Q ={1,2,3,4,5,6,7,8,9,10,11,12}, and:
2. P ⋂ Q = Φ, and:
3. The number of elements of P is not an element of P, and:
4. The number of elements of Q is not an element of Q

Find N.

(In reply to re: Answer only by Daniel)

You are right.

I've solved it too fast, trying a 5-element set, and justifying the

 2^(n-2) answer.

Please see my edited version.

Posted by Ady TZIDON on 2015-04-13 15:41:50