0 1 -------------- 0| 0 0 1| 0 0 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 0 1| 0 1 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 0 1| 1 0 (1*0)*1 = 0 but 1*(0*1) = 1 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 1 1| 0 0 (1*0)*1 = 1 but 1*(0*1) = 0 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 0 1| 0 0 (0*0)*1 = 0 but 0*(0*1) = 1 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 0 1| 1 1 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 1 1| 0 1 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 0 1| 0 1 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 1 1| 1 0 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 0 1| 1 0 (0*0)*0 = 1 but 0*(0*0) = 0 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 1 1| 0 0 (0*0)*0 = 0 but 0*(0*0) = 1 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 0 1 1| 1 1 Semigroup ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 0 1| 1 1 (0*0)*0 = 1 but 0*(0*0) = 0 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 1 1| 0 1 (0*0)*0 = 0 but 0*(0*0) = 1 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 1 1| 1 0 (0*0)*1 = 0 but 0*(0*1) = 1 ~~~~~~~~~~~~~~~~~~~~ 0 1 -------------- 0| 1 1 1| 1 1 Semigroup ~~~~~~~~~~~~~~~~~~~~