 Hi and welcome to the session. I am Asha and I am going to help you with the following version which says If A is a set having all those x such that x is a natural number B is a set having all those x such that x is an even natural number C is a set having all odd natural numbers and a set D having all prime numbers and we are required to find these six parts. So first let us learn what does intersection of two sets mean. Suppose we have any two sets A and B then intersection of A and B is equal to all those x such that x belongs to A as well as x belongs to B. That is all those elements which are common to both A and B belong to the set A intersection B. So this definition is a key idea that we will be using in this problem to solve it. Let us now start with the solution is a set having all those x such that x is a natural number. So the set will have elements 1, 2, 3, 4, 5, 6 and so on and the set B have all those x such that x is an even natural number. So the smallest even number which is a natural number is 2 and we have 4, 6, 8, 10, 12 and so on. So this is set B and set C and all those x such that x is an odd natural number. So the C will have elements 1, 3, 5, 7, 9 and so on. And lastly D is a set which have elements x such that x are all prime numbers. That is the set D will have 2 is the smallest prime number then we have 3, 5, 7, 11 and so on. Let us now start with the first part where we have to find the intersection of A and B. Now A is a set having all the natural numbers that is 1, 2, 3, 4, 5 and so on and B is a set having all the even natural numbers which have 2, 4, 6, 8, 10 and so on. And to find the intersection of A and B we will have to find all those elements which are common to both A and B and the numbers are 2, 4, next number is 6 and thus we have 2, 4, 6, 8, 10 and so on. And these are even natural numbers so all those x such that x is an even natural number and this set is set B thus we can say that A intersection B is equal to B. So this completes the first part and now proceeding on to the second part we have to find the intersection of A and C. Now A is a set having all the natural numbers so A is 1, 2, 3, 4, 5 and so on and C is a set having all the odd natural numbers and which are 1, 3, 5, 7, 9 and so on. Now to find the intersection of A and C we will find all the elements which are common to both A and C and the elements are 1, 3, 5 and so on. And these numbers are all odd natural numbers so all those x such that x is an odd natural number which is set C thus A intersection C is equal to set C. So this completes the second part and now proceeding on to the third part where we have to find A intersection B. Now A is a set having all the natural numbers that are 1, 2, 3, 4, 5, 6 and so on and these are set having all the prime numbers which are 2, 3, 5, 7 and so on. Now A intersection B we have all those elements which are both in A and B the elements are 2, 3, 5 and so on which are all prime numbers that is all those x such that x is a prime number and this is set D. Hence A intersection D is equal to the set D. So this completes the third part. Now proceeding on to the fourth part where we have to find B intersection C. Now B is a set having all those x such that x is an even natural number so we have 2, 4, 6, 8, 10 and so on and C is a set having all those x such that x is an odd natural number so we have 1, 3, 5, 7, 9 and so on. Now B intersection C will have all those elements which are common to both B and C and observing we find that there is no element which is common to both B and C so B intersection C is equal to 3. So our answer is intersection of B and C is an empty set which completes the fourth part. Now proceeding on to the fifth part which is B intersection D. Now B is a set having all even natural numbers so 2, 4, 6, 8, 10 and so on and D is a set having all the prime numbers so 2, 3, 5, 7, 11 and so on and we have to find the intersection of sets B and D. That is all those elements which are common to sets B and D so the common element on observing we find that is only 2 so the intersection of B and D is a set having all the element 2. So this is our answer and now proceeding on to the sixth part where we have to find C intersection D. Now C is a set having all the odd natural numbers so C is 1, 3, 5, 7, 9, 11 and so on and D is a set having all the prime numbers. Which are 2, 3, 5, 7, 11 and so on C intersection D which will have all the elements which are common to both C and D and the elements are 3, 5, 7, 11 and so on. And these are all those X such that X is an odd prime number so these all are prime numbers and also not divisible but 2 so these are odd numbers. Thus C intersection D will be the set X such that X is an odd prime number. So this completes the last part and in station hope you enjoyed it take care and have a good day.