Solutions To Mathematics Textbooks/Proofs and Fundamentals/Chapter 7

Section 7.1

7.1.2

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

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