 Hello and welcome to the session. In this session we discussed the following question which says, state the cardinal number of the following sets. We have first a set A equal to set of the letters in the word umbrella. Then next we have a set B equal to the set containing the elements X such that X plus 1 equal to 0 where X belongs to N that is the set of natural numbers. Before we move on to the solution let's first define the cardinal number of the set. We have the number of distinct members of a set is called the cardinal number of the set. So a cardinal number of a set say A is denoted by N of A. This is the key idea that we use in this question. Let's move on to the solution now. First we have a set A which is the set of the letters in the word umbrella. So the set A would be equal to the set containing the elements U, M, B, R, E, L and A. Since the repetition of the elements are not allowed in the set so we are writing the letter L only once. Though it is repeated two times in the word umbrella. Let us now count the number of distinct elements in the set A. It's 1, 2, 3, 4, 5, 6, 7. Since according to the definition we have that the cardinal number of a set is the number of distinct members of a set. So we can say that the cardinal number of the set A which is denoted by this is equal to 7. This is the answer for the first part. Now we have the second part in which we have a set B that is equal to the set containing the element X such that X plus 1 is equal to 0. Where this X belongs to the set of natural numbers N. Now since X belongs to N this means that X would take the values from 1, 2, 3 and so on. But we know that minus 1 plus 1 is equal to 0 and this minus 1 does not belong to N. So this means that there is no number or no natural number which when added to 1 gives us 0. Thus the set B is equal to 5 that is it is an empty set. Also the cardinal number of the empty set is 0. Thus cardinal number of the set B is equal to 0 since set B is an empty set. So this is the answer for second part of the question. So this completes the session. Hope you have understood the solution of this question.