 Hi and welcome to the session. My name is Shashi and I am going to help you to solve the following question. Question is show that none of the operations given above has identity. Fifth part of the previous question is A star B is equal to AB upon 4 where star is the binary operation on set Q of rational numbers. First of all let us understand the key idea to solve the given question. Given a binary operation star from A cross A to A and element E belonging to A if it exists is called identity of the operation star if A star E is equal to A is equal to E star A for every A belonging to set A. Let us now start with the solution. You know on set Q binary operation star is defined as A star B is equal to AB upon 4. Now let E be the identity element in Q where Q is the set of rational numbers then from key idea you know A star E is equal to A is equal to E star A for every A belonging to Q. Let us now find out A star E it is equal to A upon 4 which must be further equal to A but this can't be possible as this is not possible so we can write there is no element E in Q with A upon 4 is equal to A for every A belonging to Q where Q is the set of rational numbers. So our final answer is there is no identity element for binary operation star. This completes the session hope you understood the session take care and goodbye.