 Hello and welcome to the session. In this session we discussed the following question that says if n of xi is equal to 100, n of a is equal to 45, n of b is equal to 75 and n of a intersection b is equal to 30, draw a Venn diagram to find n of a union b, n of a union b complement, n of a minus b and n of b minus a. Let's proceed with the solution now. We are given n of xi that is the number of elements in the universal set is equal to 100, n of a number of elements in the set a is 45, n of b that is number of elements in the set b is 75 and n of a intersection b that is number of elements present in the set a intersection b is 30. We need to draw a Venn diagram to find n of a union b, n of a union b complement, n of a minus b and n of b minus a. Now to draw the Venn diagram first of all we will draw the universal set by drawing a rectangle. This is the universal set xi. Now the sets a and b are the intersecting sets so we will draw two intersecting circles to represent the sets a and b. These are the two intersecting sets a and b. Now since we have the number of elements in a intersection b is 30 so we write 30 in this common portion of the sets a and b. Now since we know that the number of elements in set a is 45 and the number of elements in a intersection b is 30 so the number of elements in this yellow portion would be 45 minus 30 which is 15 also in the same way as the number of elements in set b is 75 and the number of elements in a intersection b is 30 so the number of elements in this green portion would be 75 minus 30 which is 45. Now let us find out the number of elements in a union b which would be equal to the number of elements in a plus the number of elements in b minus the number of elements in a intersection b that is this is equal to 45 plus 75 minus 30 which is equal to 90 or you can say we get number of elements in a union b as 15 plus 30 plus 45 which is also 90 so thus we get the number of elements in a union b as 90. Next we will find out the number of elements in a union b complement this gray portion represents a union b complement. Now the number of elements in a union b complement would be given by number of elements in xi that is the universal set minus the number of elements in a union b. We know that the number of elements in the universal set xi is 100 so 100 minus 90 is 10 thus the number of elements in a union b complement is 10 so we have 10 here so this is the answer for the second part. Now next we have number of elements in a minus b you're supposed to find this a minus b is this yellow portion which shows that the number of elements in set a that are not present in set b so we have number of elements in a minus b is equal to the number of elements in set a minus the number of elements in a intersection b and so this is equal to 45 minus 30 which is equal to 15 so number of elements in a minus b is 15 this is the answer for the third part as you can see in the Venn diagram also this portion represents 15 elements. Next we have to find out the number of elements in b minus a this green portion represents b minus a number of elements in this is 45 so we have number of elements in b minus a is given as number of elements in b minus the number of elements in a intersection b which is 75 minus 30 this is equal to 45 so number of elements in b minus a is 45 this is the answer for the fourth part so with this we complete the session hope you have understood the solution of this question