 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says, are the following pairs of statements negations of each other? The number x is not a rational number, the number x is not an irrational number. So first let us learn the concept of negation of a statement. The denial of a statement is called the negation of a statement. One of the techniques to deepen the understanding of the mathematical statement is denial of a statement. This technique is to ask not only what it means to say that a given statement is true but also what it would mean to say that the given statement is not true. In this question we shall first write the negation of the first statement and then compare it with the second statement to decide if the pairs of statements are negations of each other or not. So let us start with the solution and in the first part the first statement is the number x is not a rational number. Now the negation of the first statement will be its denial that is the number x is a rational number. So this implies that the number x is not an irrational number, the numbers are divided into two classes. One is rational numbers, the numbers which are not rational are irrational numbers. So here the negation of the first statement is the number x is a rational number which implies that it is not an irrational number and this is the second statement and hence the given two statements in the first part are negations of each other. Thus our answer is the given pairs negations of each other. So this completes the first part. The first statement of second part is the number x is a rational number. Now the negation of the first statement is the number x not a rational number. It implies x is an irrational number since the numbers which are not rational are irrational numbers and this is the second statement that the number x is an irrational number. Thus we can say that these two statements are also negations of each other. Hence our answer is given pairs in the second part are negations of each other. So this completes the session. Hope you have understood it. Take care and have a good day.