Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 7

Section 7.1

7.1.2

(2) The binary operation * in $\mathbb {R}$  defined by $x*y=x+2y$  $\forall x,y\in \mathbb {R}$

Answer: The binary operation * in $\mathbb {R}$ is not commutative, counter example: With $2,3\in \mathbb {R}$: $2*3=2+2(3)=8$ and $3*2=3+2(2)=7$ Like $7\neq 8$, the definition of commutativity is not satisfied.