Answer to Question #191100 in Discrete Mathematics for Rainier Dan

Question

A = Q, (a*b) = a + b

Answer 1

$A=Q\left(a\cdot b\right)=a+b$

In the above expression, the identity element of the binary operation is zero.

From the identity's explanation e is the identity element if; $a\cdot e=a=e\cdot a$

The binary operation in our case will be: $a\cdot b=a+b-ab$

Letting e to be the binary element we get :

$a\cdot e=a\:\:$

$a+e-ae=a$

By subtracting a from both sides we get:

$e-ae=0\:$

$e\left(1-a\right)=0$

$a=1\:and\:e=0$

Therefore, the value of a can not be equal 1 because the binary operation * defined on Q-( 1 ).