 Hi and welcome to the session. I am Shashi. Let us do one question. Question is show that none of the operations given above has identity. First part given in the previous question is A star B is equal to A minus B, where star is the binary operation on the set Q of rational numbers. First of all, let us understand the key idea to solve the given question. Given the binary operation star from A cross A to A, an element E belonging to A if it exists is called identity for the operation star if A star E is equal to A is equal to E star A for every A belonging to A. This is the key idea to solve the given question. Let us now start with the solution. We know on Q where Q is the set of rational numbers, binary operation star is defined as A star B is equal to A minus B. Now, let E with the identity element in Q. A star E must be equal to A must be equal to E star A for every A belonging to set of rational numbers. Now, we know A star E is equal to A minus E and E star A is equal to E minus A. But A minus E is not equal to E minus A since subtraction on rational numbers is not commutative. So, we can write there is no element E in Q where Q is the set of rational numbers with A minus E equal to E minus A for every A belonging to Q. So, we can write there is no identity element for binary operation star. So, this is our required answer. Hope you understood the session. Take care and goodbye.