 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says is it true that for any six A and B power set of A union power set of B is equal to power set of A union B justify your answer. First let us learn what is the power set. This is take a set A where power set of A will be collection of all subsets of A and it is denoted by this sign. So with this idea we will solve the above problem. So this is our key idea. And with the solution we will show that power set of A union power set of B is not equal to power set of A union B. And to show this let us take one contrary example where A is a set having elements 1 and 2 and B is a set having elements 2 and 4. And power set of A which is the collection of all the subsets of A will have elements 1 set having element 2 set having elements 1, 2 and an empty set. This is power set of A. Now let us write down what is power set of A union power set of B. So this will have all those elements which are either in power set of A or power set of B or in both. These elements are set having elements 1, other set having elements 2 and 4, set having elements 1, 2, set having elements 2 and 4 and 5. Now let us find out what is A union B. Then we will find the power set of A union B. Now A union B will have elements which are either in A or in B or in both. So these elements are 1, 2 and 4. And now let us write down power set of A union B which will be having the elements as follows. Element 2, 4 like this. Now let us compare power set of A union B and power set of A union power set of B. On comparing these two we find that set having elements 1, 2 and 4 is in power set of A union B but not in the power set of A union power set of B. Element 1, 2 and 4 does not belong to power set of A union power set of B but set having elements 1, 2 and 4 belongs to power set of A union B and thus we say that power set of A union power set of B is not equal to power set of A union B. Hence justify it. So this completes the solution. Hope you enjoyed it. Take care and bye for now.