 Hello and welcome to the session. In this session we discuss the following question that says if A is equal to the set containing the elements 4, 5, 7, 8, 10 and B is the set containing the elements 4, 5, 9 and C is the set containing the elements 1, 4, 6, 9 then verify A intersection B the whole, intersection C is equal to A intersection B intersection C the whole. Before we move on to the solution, let's see what is the intersection of the two sets A and B. A intersection B is written as this and this is the set containing the elements X such that X belongs to the set A and X belongs to the set B that is A intersection B is a set that contains the elements that are both in set A and in set B or you can say that it represents the set that contains the common elements of the sets A and B. This is the key idea that we use for this question. Let's move on to the solution now. We have a set A that contains the elements 4, 5, 7, 8, 10, set B that contains the elements 4, 5, 9 and a set C that contains the elements 1, 4, 6, 9. Now we are supposed to show that A intersection B the whole intersection C is equal to A intersection B intersection C the whole. First let us find out what is A intersection B. A intersection B would contain the elements that are common to the sets A and B. Now if you observe the sets A and B then you can see that their common elements are 4, 5. So this means A intersection B is the set containing the elements 4 and 5. Now let's see what is B intersection C. B intersection C would contain the elements that are common to the sets B and C. Now if you observe the sets B and C we find that 4 and 9 are the common elements of B and C. So B intersection C is the set containing the elements 4 and 9. Now next we will find the intersection of A intersection B with the set C. This would be the set containing the common elements of A intersection B and the set C. Now from these two sets we observe that only 4 is the common element. So A intersection B the whole intersection C is equal to the single term 4. Now let this be the result 1. Next we will find out the intersection of A with B intersection C. This would be the set containing the elements that are common to the sets A and B intersection C. Now if you observe the two sets we find that only number 4 is common to both the sets. So A intersection B intersection C whole is the single term 4. Let this be result 2. Now from the results 1 and 2 we find that they are equal that is A intersection B the whole intersection C is equal to A intersection B intersection C the whole. So this is what we were supposed to verify. So hence verified. This completes the session. Hope you have understood the solution of this question.