 Hello and welcome to the session. In this session, we discuss the following questions with safe, state, which of the following sets are finite and which are infinite. The first set that we have is the set of all days in a week. The second set is, set containing the element x such that x is equal to 3y where y belongs to w. Then we have the set containing the element x such that x is equal to y plus 1 where y belongs to n and y is greater than equal to 1 and less than 4. Before we proceed with the solution, let's first define a finite set and an infinite set. So first we have the definition for the finite set, a set which contains a definite number of objects that is in which the counting comes to an end, a finite set. Next we have the definition for the infinite set. If the process of counting the elements of a set cannot come to an end, it is an infinite set. This is the key idea that we would use for this question. Now we move on to the solution. First we have the set of all days in a week. Let us check whether this set is a finite set or an infinite set. Now we know that since the number of days in a week are 7 which is finite, so therefore the set of all days in a week is a finite set. The set that we have is the set containing the element x such that x is equal to 3y where this y belongs to the set of whole numbers w. Now since y belongs to w, that is the set of whole numbers, this means that we have y is equal to 0, 1, 2, 3 and so on. That is y would take infinite values. So we have that y takes infinite values. Also x is equal to 3y, therefore x would also take infinite values since y is taking infinite values. This means that this set would have infinite elements. That is the set containing the element x such that x is equal to 3y where y belongs to w would contain infinite elements and the process of counting the elements of this set would not come to an end. This means that the given set is an infinite set. Now next we have the set containing the element x such that x is equal to y plus 1 where y belongs to n and y is greater than equal to 1 and less than 4. Now that we have y belongs to n and y is greater than equal to 1 and less than 4. This means that y would take the values 1, 2 and 3 and we also have x is equal to y plus 1. Therefore for y equal to 1, 2 and 3 we obtain certain values of x like when we have y equal to 1 we get the value of x as 2 and for y equal to 2 we get the value of x as 3 and for y equal to 3 we get the value of x as 4. So for y equal to 1, 2 and 3 we obtain the values of x as 2, 3 and 4. Thus we can say that the given set containing the element x such that x is equal to y plus 1 where y belongs to n and y is greater than equal to 1 less than 4 is same as the set containing the elements 2, 3 and 4 that is the values of x. So as you can see that this set is a finite set since it contains a definite number of objects. Therefore we can say that the set containing the element x such that x is equal to y plus 1 where y belongs to n and y is greater than equal to 1 and less than 4 is a finite set. Thus we get the first set given that is the set of all days in a week is a finite set. Then the second set given is an infinite set then the third set given is again a finite set. So this completes the session. Hope you have understood the solution of this question.