given 2 set D , E
[tex]\begin{gathered} D=(2,3,5,7)\text{ } \\ E=(0,1) \end{gathered}[/tex][tex]\begin{gathered} C(D)=4 \\ C(E)=2 \\ C(D\times E)=4\times2=8 \\ C(E\times D)=2\times4=8 \end{gathered}[/tex]now to show that,
[tex]C(D\times E)=C(E\times D)=C(D)\ast C(E)[/tex]subsitute the known values as given below,
[tex]\begin{gathered} C(D\times E)=C(E\times D)=C(D)\ast C(E) \\ 8=8=4\times2 \\ 8=8=8 \end{gathered}[/tex]thus, we have shown that,
[tex]C(D\times E)=C(E\times D)=C(D)\ast C(E)[/tex]