 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says, let F pay a subset of Z plus Z, defined by F is equal to the set of ordered pair AB, A plus B such that A and B are elements of Z is F a function from Z to Z justify your answer. Before proceeding on with the solution of this problem, let us first learn what is a function. A function from A to a set B is a specific type of relation for which every element X of A has one and only one image Y in set B. That is we write a function F such that from the set A to the set B where F X is equal to Y where X is an element of set A and Y is an element of set B. So with the help of this definition we are going to solve the above problem. So this is a key idea. Let us now start with the solution. Now here we are given that is a subset of Z cross Z which is defined by for ordered pair AB, A plus B such that A and B belong to Z and we have to determine F a function from Z to Z. Now as F is a subset of Z cross Z this implies F is a relation from Z to Z. Since a relation from Z to Z is the Cartesian product of the subset from Z to Z so AB, A plus B such that AB belongs to Z is an ordered pair of F. A is equal to 0 and B is not 0 and B belongs to Z. Then ordered pair which is AB, A plus B is equal to 0, B which belongs to F let A is not 0 and B an element of Z B is equal to 0. Then the ordered pair which is AB comma A plus B will become 0 comma A which belongs to F and this shows that the element 0 which is the first element has two different images A and B. This shows the element which is the first element of the ordered pair different images. A not equal to B and therefore F is not a function and the answer is so this completes the solution hope you enjoyed it take care and bye for now.