Question

A binary operation * is defined on the set R of real numbers by x*y=x+y xy where x,y belongs to R. Find, under the operation *, the identity element

Answer 1

[AI-generated answer — Bot GPT 3.5]

The identity element for a binary operation * is defined as the element e such that x*e = x and e*x = x for all x in the set.

In this case, we have x*y = x+y and x*y = xy for x, y in R.

For the identity element e, we want x*e = x for all x in R:

x*e = x+e = x (by definition of *)

This equation holds true for all x if and only if e = 0. Therefore, the identity element for this operation * on the set R of real numbers is 0.