 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says which of the following statements are true and which are false. In each case give a valid reason for saying so. The first statement is P that is each radius of a circle is a chord of the circle. A answer to the first part would be this statement is false because by definition of the chord it should intercept the circle in two points. So our answer to the first part is this. Now second part is Q that is the center of a circle bisects each chord of the circle. Our answer to the second part would be this is a false statement. Now this can be shown by giving a counter example a chord which is let us just write down that this can be shown by giving a counter example because a chord which is not a diameter gives the counter example. So we see that the center of a circle does not bisect each chord of the circle. Now the third part is the statement R that says that circle is a particular case of an ellipse. The answer would be that this statement is true. We know that the standard equation of an ellipse having center at the origin and major and minor axis of lens 2a and 2b along the coordinate axis is x square by a square plus y square by b square equals to 1. Now if a is equal to b then this reduces to x square by a square plus y square by a square equals to 1 or we can say x square plus y square equals to a square which is the equation of a circle. So we can say that in the equation of an ellipse if we put a equal to b then it is a circle. Now let us see the solution to fourth part. The fourth statement is s that is if x and y are integers such that x is greater than y then minus x is less than minus y. Our answer would be that this is a true statement and this we can get directly by rule of inequality. So if we have the statement x is greater than y now according to a rule of inequality both sides of an inequality is multiplied or divided by same negative in number then the inequality is changed. So when we multiply by minus 1 we get x minus x is less than minus y therefore the statement is true. Now the fifth statement is statement t that is square root of 11 is a rational number our answer is false since 11 is a prime number therefore root 11 is irrational because square root of a number is rational only when the number is a perfect square and 11 is not a perfect square so it is prime so square root 11 is irrational. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.