 Hello and welcome to the session. In this session we will discuss the following question and the question says, let U is equal to the set containing X such that X is an integer where minus 5 is less than X is less than equal to 10, B the universal set let A is equal to the set containing the elements 2, 4, 6, 8, D is equal to the set containing the elements 1, 3, 5, 7, C complement is equal to the set containing the elements minus 4, minus 3, minus 2, minus 1 and D is equal to the set containing the elements 5, 6, 7, 8, 9, 10. Find first D complement, second C, third D complement, fourth number of elements in A complement and fifth number of elements in C. Before we start solving the question let us first recall what is complement of a set. Complement of a set A is the set of elements in the universal set which are not in A. It is denoted by, so this is the key idea for this question and using this key idea we shall solve the question. Let us start the solution now. We are given U is equal to X such that X is an integer where minus 5 is less than X is less than equal to 10 as the universal set. Let us first list down the elements of the set U. So U is equal to the set containing minus 4, minus 3, minus 2, minus 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Now in the first part we have to find what is B complement. We are given that B is equal to the set containing the elements 1, 3, 5, 7. So we have B is equal to the set containing 1, 3, 5, 7. So using the key idea we have B complement contains all the elements of the universal set U which are not in B. That is B complement contains all the elements of U except the elements 1, 3, 5, 7. So B complement contains all these elements except 1, 3, 5 and 7. So we have B complement is equal to the set containing minus 4, minus 3, minus 2, minus 1, 0, 2, 4, 6, 8, 9 and 10. This is the solution for the first part. Now in the second part we have to find C. We are given in the question that C complement is equal to the set containing minus 4, minus 3, minus 2 and minus 1. That is we have C complement is equal to the set containing minus 4, minus 3, minus 2, minus 1. Also we know that C is equal to complement of C complement. That is C contains all the elements of the universal set U except for the elements in C complement that is minus 4, minus 3, minus 2 and minus 1. So C contains all these elements in the set U except for the elements minus 4, minus 3, minus 2 and minus 1. Therefore we have C is equal to the set containing the elements 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This is our solution for the second part. Now in the third part we have to find what is D complement. We are given that D is equal to the set containing the elements 5, 6, 7, 8, 9, 10 as D is equal to the set containing the elements 5, 6, 7, 8, 9, 10. So D complement contains all the elements of the universal set U except for the elements which are in D. That is all these elements except for the elements 5, 6, 7, 8, 9 and 10. Therefore D complement is equal to the set containing the elements minus 4, minus 3, minus 2, minus 1, 0, 1, 2, 3 and 4. Now in the fourth part we have to find number of elements in the set A complement. Now we are given in the question that A is equal to the set containing the elements 2, 4, 6, 8. So A complement contains all the elements of the universal set U except for the elements which are in A. That is all these elements except for the elements 2, 4, 6 and 8. Let us now list down the elements of A complement. We have A complement is equal to the set containing the elements minus 4, minus 3, minus 2, minus 1, 0, 1, 3, 5, 7, 9 and 10. Therefore the number of elements in A complement is 11. That is the answer for this part is number of elements in A complement is equal to 11. Now in the fifth part we have to find number of elements in C. In the second part we found the set C and we can see that C contains 11 elements so we can say that since the number of elements in C is 11 therefore the answer is number of elements in C is equal to 11. With this we end our session. Hope you enjoyed the session.