 Hello and how are you all today? My name is Priyanka and I shall be helping you with the following question. It says identify the quantifier in the following statement and write the negation of the statements. Now here we are given three statements in this question. The first statement says there is exist a number which is equal to its square. For every real number x, x is less than x plus 1 and then there exist a capital for every state in India. Before proceeding on we should be well versed with the term or the concept of quantifier. Quantifiers are phrases like there exist or sorry for all in the statement. Now as we know what a negation of statement is for example New Delhi is a city. So the negation of the statement is it is not the case that New Delhi is a city. That is that can be also written as it is false that New Delhi is a city or simply we can express it as New Delhi is not a city. So while forming the negation of a statement phrases like it is not the case, it is false, no, etc are used. So these are the few key concepts let us proceed on with our solution. Now here the first statement given to us is it is there exist a number which is equal to its square. Now in this statement the quantifier is there exist and the negation of the statement is there does not exist a number which is equal to its square. Right so here we have used does not change the given statements into the negation right into its negation. So this completes the first part statement says for every one. So here the quantifier of the statement is there exist a real number such that X is not this one. So to write down the denial of this statement we have used not in the statement and rearranged it to form its negation. Right so this completes the second part. Third statement says there exist capital for every state in India now its quantifier is there exist which does not right. So this is a denial of the above given statement that forms a negation of the statement. This ends my session hope you understood the question well firstly you need to identify the quantifier and then write down the negation of the statement given to us hope you can solve more have a nice day. Thank you.