 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says, let a be a set having elements 1, 2, 3, 4 and b be a set having elements 1, 5, 9, 11, 15 and 16 and f be a set having elements for a quiz type 1, 5, 2, 9, 3, 1, 4, 5, 2, 11 are the following true. First is f is a relation from a to b and second is f is a function from a to b. Justify your answer in each case. So, let us start with the solution and here we are given two sets a and b having elements 1, 2, 3, 4 and 1, 5, 9, 11, 15 and 16 respectively and f is a set having ordered pairs 1, 5, 2, 9, 3, 1, 4, 5 and 11. We have to check whether it is true or not as f is a relation a to b. First let us learn what is a relation. Suppose we have any two sets a and b, then the relation r from the set a to b is a subset of the Cartesian product of a and b which is obtained by describing the relation between the first element and second element of the ordered pair a cross b and here we see that f which is a set having ordered pairs 1, 5, 2, 9, 3, 1, 4, 5, 2, 11, the first element of the ordered pairs 1, 2, 3 and 4 and set elements of the ordered pair are 5, 9, 1, 5 and 11. Now all these elements are of set a and 5, 9, 1, 5 and 11 are elements of set b. You can say that all the first elements belong to set a and again elements of the ordered pair belong to set b. Hence this is a subset of the Cartesian product of a and b, therefore f is a relation. So this complete and now proceeding on to the second part f is a function from a to b. f is a set having ordered pairs 1, 5, 3, 1, 4, 5 and 2, 11. Now a function from a set a to b is a specific type of relation for which every element x of a has one and only one image y in set b. Then here fx is equal to y so this is a function and here that the pairs 2, 9 and 2, 11 have the same first element. There is a that we can say that for an element 2 which is set a it has two images and thus this implies that f is not a function. Hence are on this? No. So this completes the second part and hence the solution. Hope you enjoyed this session. Take care and have a good day.