 Hi and welcome to the session. My name is Shashi. Let us do one question. Question is, let star-vita binary operation on the set 1, 2, 3, 4, 5 defined by a star-b is equal to hf of a and b. Is the operation star- same as operation star defined in exercise 4 above? Justify your answer. First of all, let us understand that for general operation star from a cross a to a, if a is equal to set of a1, a2, till a n, then the operation table will be having n rows and n columns with ijth entry being ai star aj, which is equal to entry in the ijth row and jth column of operation table. This is the key idea to solve the given question. Let us start with the solution now. The given set in the question is 1, 2, 3, 4, 5 and star- is defined on the set by a star-v equal to hcf of a and b. Now we know the number of elements in the set is equal to 5, so we had made 5 rows and 5 columns. Now we will make the operation table. We know hcf of 1 and 1 is 1, so we get here 1. hcf of 1 and 2 is 1, hcf of 1 and 3 is again 1. Similarly, hcf of 1 and 4 is 1, hcf of 1 and 5 is equal to 1. Now we will fill the second column. hcf of 2 and 1 is 1, hcf of 2 and 2 is 2, hcf of 2 and 3 is 1, hcf of 2 and 3 is 1, hcf of 2 and 4 is 2, hcf of 2 and 5 is 1. Now we will fill the third column. hcf of 3 and 1 is equal to 1, hcf of 3 and 2 is equal to 1, hcf of 3 and 3 is 3. hcf of 3 and 4 is again 1, hcf of 3 and 5 is equal to 1. Now we will fill the fourth column. hcf of 4 and 1 is equal to 1, hcf of 4 and 2 is equal to 2, hcf of 4 and 3 is equal to 1, hcf of 4 and 4 is equal to 4, hcf of 4 and 5 is equal to 1. Now we will fill the fifth column. hcf of 5 and 1 is 1, hcf of 5 and 2 is 1, hcf of 5 and 3 is 1, hcf of 5 and 4 is equal to 1 and hcf of 5 and 5 is equal to 5. So this completes the operation table. Now this table gives the star dash operation. Now we have been asked in the question if star dash operation is same as operation star defined in exercise 4 above. Now the star operation defined in exercise 4 above is shown by this table. Now we can see that both the tables are same. So we can say star operation is same as star dash operation. Since operation table, star dash operation, therefore star and star dash are same. So our required answer is yes, star and star dash are the same operations. This completes the session. Goodbye and take care.