Question

prove that *R×R- define by a*b=a+2b is not associative​

Answer 1

Prove:

let this function operate on x,y and z.

Now,

x*(y*z)

= x+2(y*z)

=x+2(y+2z)

= x+2y+4x

(x*y)*z

=(x*y)+2z

=x+2y+2x

Since,

x*(y*z) $\neq$(x*y)*z

It's not associative.