 Hi and welcome to the session. I am Asha and I am going to help you with the following question that says, assume that power set of A is equal to power set of A, show that A is equal to B. So first let us learn what is a power set. Any set, the collection of all the subsets of A is called the power set of A which is denoted by P of A. So this is the solution we are going to use in this problem to show that set A is equal to set B. So this is our key idea. Let us now start with the solution and there we have given the power set of A is equal to the power set of B. So let X be any subset of set A. This implies X belongs to the power set of A and since power set of A is equal to power set of B, this further implies that X belongs to the power set of B which implies that X is a subset of set B, small X be any arbitrary element of the set X. This implies X belong to the set A and also this implies that X belongs to the set B. As we can say that all the elements which belong to the set A belong to B also and vice versa. Hence A is a subset of B and B is a subset of A. This means that A and B exactly have the same elements and thus set A is equal to set B. So this completes the solution. Hope you enjoyed it. Take care and have a good day.