 Hi and welcome to the session, I am Asha and I am going to help you with the following question which says, in the following state whether A is equal to B or not. So first let us learn what are equal sets. Two sets are said to be equal exactly the same elements. The sets are called unequal sets that is those sets which are not equal sets are unequal sets. So this is the key idea we are going to use in this problem to find a solution. Take a solution, the first one is A is a set containing elements A, B, C and D and B is the set containing elements D, C, B and A. Now we see that these two sets have exactly the same elements A is in the set A also and B also, B is also in the set A also and B also, C is also in the set A and B and D is also in the set A and B. So both the sets A and B contain four elements which are exactly the same thus we can say yes A is equal to B. This completes the first part and now proceeding on to the second part is equal to 4, 8, 12 and 16 and B is the set which contains elements 8, 4, 16 and 18. Now when observing these two sets we find that there are four elements in set A and four elements in set B but 12 element of set A is not an element of set B. Similarly here 18 which belongs to set B does not belong to set A so this implies these two sets are unequal hence the answer is no the set A is not equal to B. So this completes the second part now proceeding on to the third part where A is the set containing elements 2, 4, 6, 8 and 10 and B is the set which contains all those x such that x is a positive even integer x is less than or equal to 10. The upper limit is 10 and we have to write all those positive integers which are less than or equal to 10. So the smallest is 2 then we have 4, 6 and 8. So this is the set B. Now when observing set A and B we find that there are five elements in both these sets and they are exactly the same thus we can say that yes set A is equal to set B. So this completes the third part and now proceeding on to the last part where A is a set which contains all those x such that x is a multiple of 10. B is the set which contains 10, 15, 20, 25, 30 and so on. Now first let us write the elements in the set A. Now A contains all those elements x such that x is a multiple of 10. So there are many multiples of 10. That is when any number multiplied with 10 results in a multiple of 10. So minus infinity is starting from then we have minus 20, minus 10, 0. 0 we get on multiplying 10 with 0 then we have 10 which we get on multiplying 10 with 1 then 20, then 30 and so on up to infinity. And observing A and B we find that 15 which is in set B is not in set A and the two sets A and B are not equal. That is our answer is no. So this completes the last part and that is the solution. Hope you enjoyed it. Take care and have a good day.