 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question. Question is, state whether the following statements are true or false. Justify if star is a commutative binary operation on n where n is the set of all natural numbers then a star bracket b star c is equal to c star b star a. First of all let us understand the key idea to solve the given question. A binary operation star on the set x is called commutative if a star b is equal to b star a for every a b belonging to set x. Now let us start with the solution. Now we know star is commutative binary operation on n. Therefore b star c is equal to c star b for every c b belonging to set n. b star c is equal to c star b we have used the key idea here. So let us name this equation as 1. Now we can write a star b star c is equal to a star c star b using equation 1. We know b star c is equal to c star b so a star b star c must be equal to a star c star b. Now a star c star b can be written as c star b star a. We are given in the question that star is a commutative binary operation on n. Here this is our a and this bracket is our b. So a star b must be equal to b star a that is what we have done here. So we get a star bracket b star c is equal to c star b star a. So the given statement is true. Thus our required answer is true. This completes the session. Hope you understood the session. Take care and goodbye.