$\text{ Let }N\text{ be the set of non-negative integers, }I\text{ the set of integers, }{N}_p\text{ the set of non-positive integers, }E\text{ the set of }$

$\text{ even integers and }P\text{ the set of prime numbers. Then }$

        $$\begin{gathered} N= \left\{0,1,2,3,.......\right\} \\ I = \left\{......,-2,-1,0,1,2,......\right\} \\ N_{p=}\left\{........-2,-1,0\right\} \\ E =\left\{2,4,6,........\right\} \\ P = \left\{2,3,5,........\right\} \end{gathered}$$   

         $\begin{array}{c}N\mathrm{\Delta }{N}_p=\left(N-N_p\right)\cup \left(N_p-N\right)\\ =\{1,2,\dots \}\cup \{\dots -2,-1\}=I-\left\{0\right\}\end{array}$