 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says find the intersection of each pair of sets. So first let us learn what is the intersection of two sets. 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 and x belongs to B also. So with the help of this definition we are going to solve the above problems. So this is our key idea. First part x is equal to a set having elements 1, 3 and 5 and y is a set having elements 1, 2 and 3. Now the common elements in x and y are 1 which is both inside x and y and 3. So x intersection y is equal to a set having elements 1 and 3. So our answer is the intersection of x and y is equal to a set having elements 1 and 3. So this completes the first part. Now proceeding on to the second part where A is a set having elements A, E, I, O, U and B is a set having elements A, B and C. Now let us find the common elements which are both in A and B. So A is the only common element. So the common element in both as we have A intersection B is equal to singleton set having only one element that is which is A. So answer of second part is A intersection B is equal to singleton set A. Now proceeding on to the third part where we have A set having all those x such that x is a natural number and as we know natural numbers begin from 1 and goes on and a multiple of 3. So A will be a set having natural numbers start from 1 and the first multiple of 3 will be 3 then we have 6, 9 and so on and set B contains all those x such that x is a natural number which is less than 6. Thus B will be a set having elements 1, 2, 3, 4 and 5. Now the common elements in A and B, A intersection B will have only one element and that is 3. So the answer of third part is A intersection B which is 3. This completes the third part and now proceeding on to the fourth part where A is a set having all those x such that x is a natural number 1 is less than x is less than or equal to 6. And B is a set having all those natural numbers 8 such that x is a natural number 6 is less than x is less than 10. So A will have the elements greater than 1 and the natural numbers so we first number is 2 and 3, 4, 5 and less than or equal to 6 and by 6 is also included in the set. Now let us write the set B which have all those x such that x is a natural number and x lies between 6 and 10. So the first number is 7 then 8 and then 9. Now observing these two sets we find that there is no common element in A and B there is no element which is both A and B. We must have A intersection B as an empty set 5. The answer of fourth part is an empty set which is 5. Now proceeding on to the last part where A is a set having elements 1, 2 and 3 and B is a set having no element that is B is an empty set. Now the intersection of any set with the empty set is always empty since there is no element in set B this implies there is no common element which is both in A and B this implies that A intersection B is an empty set which is 5 and thus answer of fifth part is A intersection B is equal to 5. So this completes the last part and ends the session. Hope you enjoyed it. Take care. Have a good day.