 Hi and how are you all today? I'm Priyanka and let us discuss the following question. It says state whether the following statements are true or false. Justify your answers. Now in each of these three cases we need to tell whether the statements given to us are two statements or false statements. The first statement says every irrational number is a real number. Second, every point on the number line is of the form root m where m is a natural number. And third, every real number is an irrational number. Now let us start with our solution. We will be rewriting these statements. The first statement says every irrational number is a real number. Now this statement is a true statement because we know that real numbers are splitted into two categories. One is rational numbers and the other are irrational numbers. So that means irrational number is a part of real number and hence every irrational number is a real number. Right so this is a true statement for the reason that since collection of real numbers is made up of rational irrational numbers. Right so this is the answer to our first part. The second part says every point on the number line is of the form root m where m is a natural number. Now this is clearly a false statement because of the reason that no negative number can be the square root of any natural number. So we know that in a number line we have both positive and both negative integers. Now every point on the number line means we can have this negative number also but we know that this negative number cannot have a square root. Hence it cannot be a natural number also. So this is a false statement. Then the third part says every real number is an irrational number. As we have discussed above also we discussed that real numbers are taken into two categories. One is rational and the other is irrational numbers. Now it is saying that every real number is an irrational number but it is not true because it can be a rational number also. Hence it will be again a false statement because for example let's take a number 2 that we know is real but is this number rational or irrational number. This is a rational number. Hence for example 2 is real but not irrational number. So that is why because of this reason we have stated that this statement is a false statement. So this completes the question that was given to us. I hope you enjoyed. Give a proper reason for saying whether a statement is a true statement or a false statement. It will help you in making your point more clearer. Bye for now.