(2) The binary operation * in R {\displaystyle \mathbb {R} } defined by x ∗ y = x + 2 y {\displaystyle x*y=x+2y} ∀ x , y ∈ R {\displaystyle \forall x,y\in \mathbb {R} }
Answer: The binary operation * in R {\displaystyle \mathbb {R} } is not commutative, counter example: With 2 , 3 ∈ R {\displaystyle 2,3\in \mathbb {R} } : 2 ∗ 3 = 2 + 2 ( 3 ) = 8 {\displaystyle 2*3=2+2(3)=8} and 3 ∗ 2 = 3 + 2 ( 2 ) = 7 {\displaystyle 3*2=3+2(2)=7} Like 7 ≠ 8 {\displaystyle 7\neq 8} , the definition of commutativity is not satisfied.
