1.4 Exercise 1

Let Ω consist of the set of positive integers. Consider the subsets

$A = \left\{\omega : \omega \leq 12\right\} B = \left\{\omega : \omega < 8\right\} C = \left\{\omega : \omega \text{is} \text{even}\right\}$

$D = \left\{\omega : \omega \text{is} \text{a} \text{multiple} \text{of} \text{3}\right\} E = \left\{\omega : \omega \text{is} \text{a} \text{multiple} \text{of} \text{4}\right\}$

Describe in terms of $A , B , C , D , E$ and their complements the following sets:

1. $\left\{1 , 3 , 5 , 7\right\}$
2. $\left\{3 , 6 , 9\right\}$
3. $\left\{8 , 10\right\}$
4. The even integers greater than 12.
5. The positive integers which are multiples of six.
6. The integers which are even and no greater than 6 or which are odd and greater than 12.