 Hi and welcome to the session. Let us discuss the following question. Question says determine whether or not each of the definition of star given below gives a binary operation in the event that star is not a binary operation. Give justification for this. Second part is on z plus where z plus is the set of all positive integers. Define star by a star b is equal to a v. Let us start the solution now. We are given a star b is equal to a v. We have to check if star is a binary operation on set of positive integers. Now, we know for all a v belonging to z plus, a v will also belong to z plus as we know product of positive integers is a positive integer only. So, we can write therefore star is a binary operation on z plus. Our required answer is yes. This completes the session. Hope you understood the session. Good bye.