Chapter 12.1, Problem 23E

Exercises 4-3 deal with the Boolean algebra {0, 1} with addition, multiplication, and complement defined at the ginning of the section. In each case, use a table as in Example 8.

23. Verify the zero property.

The Boolean operator $\oplus$ , called the XOR operator, is defined by $1\oplus 1=0$ , $1\oplus 0=1$ , $0\oplus 1=1$ , and $0\oplus 0=0$ .