 Hi and welcome to the session. I am Priyanka and let us do the following question together. It says let A is equal to 1, 2, 3, 4, 5. Which of the following statements are incorrect and why? So first of all we need to tell which of the statements are incorrect and then we need to justify our answers. These are the 11 parts of the question which are given to us and we need to mention whether they are correct or incorrect one by one. But before proceeding on with the solution we can see very different symbols coming out here. Now we must know what does this symbol means and what does this symbol means? They are two different symbols. This is symbol of is a subset of. So if you want to say that yes this is a subset of this then we write the names of the two sets and then insert this sign between them. This means it is a symbol of belongs to, belongs to means that yes this element belongs to this set. Now here we are talking about two sets and between two sets only we can use this symbol and in this we use it between an element and a set. So belongs to is always between an element and a set and we use this symbol between two sets only. So the knowledge of these symbols are the key ideas we are going to use in order to proceed on with our solution. So let us start with our first part. Now it says 3 comma 4 is a subset of A. Now we need to tell whether this statement is a correct statement or not. Since 3 does not belongs, this symbol means it does not belongs to. Since we know 3 does not belongs to A and 4 does not belongs to A we can say that this statement is incorrect. We see that 3 and 4 is an element of A. If we carefully analyze the set which is given to us 3 comma 4 embraces in curly brackets is one of the element. They are not two elements. So we can write that 3 and 4 separately are not elements of A. So this statement is an incorrect statement. Proceeding on to the next part. Now here we are. Now tell whether 3 comma 4 belongs to A or not. Now we know that 3, 4 is an element of A. This is an element and this is a set. So we can have a sign belongs to between an element and a set and since it is fulfilling this criteria. So we can write that this is a correct statement. So we observe that 3, 4 is an element of the given set that is A and hence we can have belongs to sign between them. Proceeding on to the third part. Now here we have 3, 4 that is an element is a subset of A. Now we know that 3, 4 is an element of A. So that means 3 comma 4 belongs to A and this is hence a subset of A also. That is the element embraces becomes a subset of A. Here it is a set and this is also a set. It is embraces if you carefully analyze. So the answer will be that this is a correct statement. Proceeding on to the next one. Now we are given that 1 is a, 1 belongs to A. Now we know that 1 is an element and A is a set. So this element belongs to this set or not. Yes, it is true that 1 belongs to A. So we simply write that this is again a correct statement which is given to us. Proceeding on with the fifth part. Now here 1 is a subset of A but 1 is not a set. It's just an element. So that means we cannot have a sign which means that it is a subset. It belongs to A but it is not a subset of A because it is not a set. 1 is a not a set. It is an element of A. So that means this is an incorrect statement. Proceeding on further to the sixth part. We are given 1, 2, 5 is a subset of A. Now we know that 1 is an element that belongs to A. 2 belongs to A as well as 5 also belongs to A as these all are elements which are present in A also. So set A contains all these elements and hence it is in braces. So that means it is a set. A is also a set. So that means we can have a subset sign between it. So that means this is a correct statement. Proceeding on to the next part. Seventh part. It says 1, 2, 5 belongs to A. The elements of 1, 2, 5 that is the element of this set belongs to A but set containing all these elements do not belong to A. This is a set and this is also a set. An element can belong to a set not a set to a set. So instead of this sign belongs to we should have a sign which says it is a subset. So that means this is an incorrect statement which is given to us as an element can only belong to a set. Proceeding on further to the eighth part we have 1, 2, 3 these are the elements of the set is a subset of A but 3 is does not belongs to set A. Since 1 of the elements of this set does not belongs to the other set. So that means it is not a subset and hence we can write that this is an incorrect statement as 3 does not belongs to A and 3 is a part of this set. Hence this set is not a subset of set A. Proceeding on further to the ninth part, 5 belongs to A. 5 is not shown to be an element of A but we know that it is a subset of every set and this sign means belongs to and not the subset. Hence it is an incorrect statement. Proceeding on further to the tenth part it says 5 is a subset of A. As we know that 5 is a subset of every set thus this means that this is a correct statement. Proceeding on further to the last and final part it says 5 in braces is a subset of A. But as we know from one of the points above 5 does not belongs to A until and unless an element does not belongs to the other set it cannot form to be an subset and this is 5 is in braces so that means this has become into a set in between two sets. We can have the subset sign but since 5 does not belongs to A that means this is an incorrect statement. So in end we can write the answer as that statements which are incorrect the first part the fifth part the seventh eighth ninth and the eleventh part right. So this completes the entire question which was given to us I hope you enjoyed the session and now can tell whether a statement is correct or incorrect giving reasons also. Bye for now.