Question

A binary operation * on the set of real numbers is defined by a*b= a+b-ab for a,b, c is belongs to R.
i) show that the operation is associative. That is, (a*b)*c=a*(b*c) for all a,b,c belongs to R.
ii) Find the value of -5*8 and also the value of (4*6)*5/13.

Answer 1

your def: a*b= a+b-ab
= first + last - product of first times last

(a*b)*c
= (a+b-ab)*c
= a+b-ab + c - ac - bc + abc
= a+b+c - ac - ab - bc + abc

a*(b*c)
= a*(b+c - bc)
= a+b+c-bc - ab - ac + abc
= a+b+c - ac - ab - bc + abc
= (a*b)*c
so the operation is associative

-5*8 = -5+8 -(-40) = 43

I think you should try the last part yourself
remember, first + last - product