 Hi, and how are you all today? Let us discuss the following question together. It says, taking the set of natural number as the universal set, write down the complement of each of the following sets. For each of the following set, we need to write down their complements. So the first part which is given to us says, X is to X is an even natural number. So that means it will be having numbers that will be 2, 4, 6 and so on. Right, now for this set we need to write its complement that will be the elements that are not present in this set and that will be the obvious answer, X is to X is an odd natural number, isn't it? Which will include elements that is 1, 3, 5 and so on. Proceeding on to the second part. Now here we need to write down the complement of the following set that is X is to X is an odd natural number. So what will it just complement? The reverse of it, that will be X is to X is an even natural number, isn't it? Proceeding on further to the third part, it says X is to X is a positive multiple of 3. So which are the positive multiples of 3? Let us write down few of them that will be 3, 6, 9, 12 and so on. Right, now we need to write the complements that will be the elements which are not present in this set and that will be X is to X belongs to natural number and X is not a positive multiple of 3. Right, it will not be. If the set which is given to us has the positive multiples of 3, its complement will not be having the positive multiples of 3. Proceeding on further to the next part, it says X is to X is a prime number. Now which are the prime numbers which are known to us? They are 2, 3, 5, 7, 11 and so on. So what will be the complement of this set which will not be having any prime number? So other than prime number, which are the numbers which we have in our number system? They are composite numbers. So X is to X is positive composite number and X is equal to 1. Hey, so this will be the answer because if you are having a set which is having prime number, then its complement will be a set which are having composite numbers that means which have factors other than the number and 1. Proceeding on further to the next part, it says X is to X is a natural number divisible by 3 and 5. So what will its complement be? X is to X is a natural number. If it is divisible by 3 and 5, we will have X is to X is a natural number and X is not. The focus point is not divisible by 3 further. X is to X is a perfect square. So what will its complement be having? It will be having is not a perfect square, right? And every number belongs to the natural number as the universal set which is given to us is a natural number itself. Proceeding on further, this is the answer. So now for this, now you tell me the answer. I am waiting for it. It will be X is to X belongs to the natural number and yes, you are absolutely right. It will be an X is not a perfect cube. Proceeding on with the 8th part, now here we are given X is to X plus 5 is equal to 8. Now we will be having elements. If we solve this equation separately out here, it will be X plus 5 is equal to 8. That gives us X is equal to 8 minus 5 which gives us the value of X as 3, right? So now here the complement set will be written in the following manner. It will be X is to X belongs to N and X is not equal to 3 because in the above set the X value of X was equal to 3. So in its complement, it will be having all the natural number except number 3, right? Proceeding on further to the next part. Here also we will solve for X first. That will be 2X plus 5 is equal to 9. 2X is equal to 4. X will be 2. So now you can easily tell me its answer and that will be X is to X belongs to the natural number group and very nice. X is not equal to 2 because in the above set X was having the value 2. And now in its complement, we will be having all the natural number except number 2. Proceeding on. Now here we are given list the elements. Here we are, our set will be the value of X is greater than equal to 7. So that will be 7, 8, 9, 10 and so on. So what will its complement? It will be having X is to X belongs to the natural number group and X is less than 7 because we do not want to include 7 also. So it will be less than 7. Proceeding on with the last and final part. X is to X belongs to N and 2X plus 1 is greater than 10. So let us find out the value 2X plus 1 is greater than 10. 2X is greater than 10 minus 1. 2X is greater than 9. X is greater than 9 by 2. So in the above given set, the value of X is greater than 9 by 2. So its answer will be X is to X belongs to the natural number group. And X has to be less than equal to 9 by 2. Now why we have this sign less than equal to? Because in the above set 9 by 2 is not included. So here we include it in its complement. So this completes the question that was given to us. I hope you enjoyed the session. Bye for now.