Question

2. Consider the binary operation *:QXQ
Q defined by a * b = a+b - ab. Prove That * is
Commutative and associative. Find the identity element of * if it exists,​

Answer 1

Step-by-step explanation:

COMMUTATIVE

TO PROVE :- a*b = b*a

a*b = a+b-ab

b*a = b+a-ba

Hence a*b = b*a

Thus * is commutative

ASSOCIATIVE

TO PROVE :- (a*b)*c = a*(b*c)

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

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

hence * is associative

Answer 2

Answer:

Step-by-step explanation:

Here is the answer