MathDB

1

Part of 1980 VTRMC

Problems(1)

1980 VTRMC #1

Source:

8/11/2020
Let ∗* denote a binary operation on a set SS with the property that (w∗x)∗(y∗z)=w∗z(w*x)*(y*z) = w * z for all w,x,y,z∈S.w,x,y,z\in S. Show
(a) If a∗b=c,a*b=c, then c∗c=c.c*c = c. (b) If a∗b=c,a*b=c, then a∗x=c∗xa*x=c*x for all x∈S.x\in S.