 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says show that the following statement is true by the method of contrapositive. The statement P is if X is an integer and X square is even then X is also even. In this question we use the method of contrapositive. The statement given is of the form if P then Q. We should first suppose that Q is false and then prove that P is also false. That is if P is not true, if Q is not true implies P is not true and thus we show the given statement to be true. This is our key idea for the question. Now let us start with the solution to the question. The statement given is P that is if X is an integer and X square is even then X is also even. This statement corresponds to two statements say P1 and Q where P1 is X square is even if X is an integer and let Q be the statement that X is even. Suppose Q is false that is Q is not true is true. This implies X is odd therefore let X be equal to 2n plus 1 which is an odd number form therefore X square will be equal to 2n plus 1 the whole square taking square on both the sides. This is equal to 4n square plus 4n plus 1 which is also odd due to presence of this extra 1 therefore P1 is false or we can say P1 not true is true thus Q is not true implies P1 is not true given that P1 implies Q hence by method of contrapositive the statement P is true. So this is what we were supposed to prove in this question. I hope that you understood the question and enjoyed the session. Have a good day.