 Hi A and how are you all today? I am Priyanka and let us do the following question. It says let U is equal to 1, 2, 3, 4, 5, 6, 7, 8, 9. These are the elements of set U. The elements of set A are 1, 2, 3, 4, B are 2, 4, 6, 8 and C are 3, 4, 5, 6. Find A complement, B complement, A union C complement, A union B complement, A complements complement and B minus C complement. Now let us first be well versed with few of the symbols that we are using. U is the universal set and all the set that is A is a subset of U. B is also a subset of U and C is also a subset of U. That means A, B, C all the three sets are the subset of this universal set. If we are talking about A complement, it means all the elements which belongs to the universal set and the elements which do not belong to set A. If I am saying A union B, then that means union of set A and set B whereas A difference B. It is a symbol of this. This is a symbol of difference of sets, right? So the knowledge of all these symbols and concepts are the key idea, key ideas which are going to help us in proceeding on with the solution. So let us start with our solution. Now the universal set is given to us as the elements 1, 2, 3, 4, 5, 6, 7, 8 and 9. So first of all we need to find out A complement. A complement will be having all the elements that do not belong to A. So they are 5, 6, 7, 8 and 9 because set A consists of the elements that are 1, 2, 3 and 4. So except these elements, its complement will be containing the elements which are not in the set A. So that means our answer of the first part will be A complement is equal to elements 5, 6, 7, 8, 9 and all these elements we have taken from the universal set. So this completes the first part of the question. Let us proceed on with the second part. Now here we need to find B complement. That means elements which do not belong to set B. Set B as known to us are elements of set B are 2, 4, 6 and 8. So that means element of B complement will be all the elements present in the universal set except these elements and they will be 1, 3, 5, 7, 9 basically all the odd numbers. So this completes the answer of the second part. Proceeding on finding the third part. Now here we need to find A union C complement. Set A consists of elements that are 1, 2, 3, 4 whereas set C consists of elements 3, 4, 5, 6. Universal set is having elements from 1 to 9. So in order to find the complement of A union C first we need to find A union C ourselves. So we have 1, 2, 3, 4, union 3, 4, 5, 6 and our answer will be 1, 2, 3, 4, 5, 6. Since 3 and 4 are present in both the sets we will be writing them once only. So A union C complement will be all the elements which are not present in A union C in comparison with the universal set and they will be till 6 we are not going to write and then it is 7, 8, 9. So the answer to the third part is A union C complement is equal to 7, 8, 9 that are the elements. Proceeding on further now we need to find union B complement. The elements of set A are 1, 2, 3, 4, B are 2, 4, 6, 8 and universal set are having elements 1, 2, 3, till 9. So let us find out A union B first that will be the union of their elements and our answer will be A union B complement will be all the elements which are present in the universal set except the elements which are present in A union B and they will be 5, 7 and 9. So the answer to the fourth part is A union B complement is equal to element 5, 7, 9. Let us proceed on. Now we need to find A complement's complement. So A complement which we have found out from the above step that was elements 5, 6, 7, 8 and 9. So A complement's complement will be all the elements which are present in universal set and are not but not the elements of A complement and that will be 1, 2, 3, 4 and this becomes the answer to the fifth part. Proceeding on with the last and final part. Now here we need to find out the complement of the difference of B and C. Set B are having elements 2, 4, 6, 8. Set C are having 3, 4, 5, 6. Universal set which is known to us are having elements 1, 2, 9. So first of all we need to find the difference of set B and C and they are all the terms which are common to both which belongs to B and not belongs to C and they are 2 and 8 because 2 and 8 are the elements which belongs to B but not C. So here we have 2 and 8 so very easily we can find B the difference of set B and C complement that will be all the elements which are present in the universal set except 2 and 8 and that will be 1, 3, 4, 5, 6, 7 and 9. So this becomes the answer to the last and final part. So this means the elements which are present in B but not in C. Just remember the symbols for what the symbol stands for and you can easily proceed on with our solution. Bye for now.