 Hi and welcome to the session. Let us discuss the following question. Question says, determine whether or not each of the definition of star, even below, gives up binary operation. In the event that star is not a binary operation, give justification for this. Fifth part is on z plus, where z plus is the set of positive integers, defined star by a star b is equal to a. Let us now start the solution. We are given a star b is equal to a. We have to find if star is a binary operation on z plus, where z plus is the set of all positive integers. Now, you can write for all a b belonging to positive integers. a will belong to set of positive integers. So, we can write a star b is equal to a belongs to z plus. So, this implies star is a binary operation. So, our required answer is yes, star is a binary operation. This completes the session. Hope you understood the session. Goodbye.