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Answer to Question #17262 in Abstract Algebra for Tsit Lam

Question #17262
Ex. 4.1. In R, define a ◦ b = a + b − ab. Show that this binary operation is associative, and that (R, ◦) is a monoid with zero as the identity element.
Expert's answer
a ◦ b belongs to R
associative because
a ◦ (b ◦ c)=a ◦
(a ◦ b) ◦ c = (a+b-ab) ◦

zero is 0
a ◦
0 ◦ a=0+a-0*a=a
so R with operation ◦ is a monoid

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