Note: * is used here instead of dot and circle addition.

Attach the certificate here:

Obviously, f is a bijective function. Let's verify that G satisfies the operation that image equals image.

f(0 * 0)= f(0)& amp； f(0)=| 1-0。 | 1-0|= 1;

f(0 * 0)= f(0)= 1；

f(0 * 1)= f(0)& amp； f( 1)=| 1-0。 | 1- 1|=0;

f(0 * 1)= f( 1)= 0；

f( 1 * 0)= f( 1)& amp； f(0)= | 1- 1 | & amp； | 1-0|=0;

f( 1 * 0)= f( 1)= 0；

f( 1 * 1)= f( 1)& amp； f( 1)=| 1- 1。 | 1- 1|=0;

f( 1 * 1)= f( 1)= 0；

All in all,