 Hello and welcome to the session. In this session, we discuss the following question which says, find the power set of the following set. Set A is equal to x such that x is equal to y minus 1, where y belongs to w and y is less than 3. First let us define the power set. The set of all possible of a set A is called the power set of A and it is denoted by P of A. And if we have that a set A contains n elements, then its power set contains 2 raised to the power n elements. This is the key idea that we use for this question. Let us proceed with the solution now. We have a set A equal to x such that x is equal to y minus 1, where y belongs to w, that is the set of whole numbers and y is less than 3. Now that we have y belongs to the set of whole numbers and y is less than 3, therefore y takes the value 0, 1 and 2. Now we have x is equal to y minus 1. So now we will find the values of x for the values for y as 0, 1 and 2. So for y equal to 0, 1 and 2, we obtain x as 0 minus 1, that is minus 1, 1 minus 1, that is 0, 2 minus 1, that is 1. So we get for y equal to 0, 1 and 2, we obtain the values of x as minus 1, 0, 1. Thus we get set A is equal to the set containing the elements minus 1, 0, 1. To find the power set of set A, we have to find all the possible subsets of this set and the set of all possible subsets of this set would be the power set of A. Now subsets of A are phi, singleton minus 1, singleton 0, singleton 1, set containing the elements minus 1, 0, set containing the elements minus 1, 1, set containing the elements 0, 1 and the set containing the elements minus 1, 0, 1, that is the set A itself. So these are the subsets of set A. Now the power set of A is denoted by P of A is the set of all possible subsets of set A, that is set containing the elements phi, singleton minus 1, singleton 0, singleton 1, set containing the elements minus 1, 0, set with elements minus 1, 1, set with elements 0, 1, set with elements minus 1, 0, 1. So this is the power set of set A. Now as you can see that the set A has 3 elements, so power set of A would have 2 raised to the power 3, that is 8 elements and these are the 8 elements in the power set of A. Thus given the set A, we have found the power set of A. So this completes the session. Hope you have understood the solution of this question.