 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says show that the statement p that says if x is a real number such that xq plus 4x is equal to 0 then x is 0 is true by method of contrapositive. Now to show the validity of the statement with if p then q by contrapositive method assume that q is false prove that p is false that is q is not true implies p is not true. So here in order to prove that p implies q it is enough to show that p is not true implies q is not true which is the contrapositive of the statement p implies q. Now here the statement p given to us is if x is a real number such that xq plus 4x equals to 0 then x is 0 this corresponds to two different statements. The first is p dash that is x is a real number such that xq plus 4x is equal to 0 and the other one is say q that is x is 0. So here we are to show that q is not true implies p dash is not true so let x not equal to 0 is true that means q is not true is true then we have to show that xq plus 4x is not equal to 0. Now xq plus 4x equals to 0 implies that x into x square plus 4 equals to 0 this implies that either x is equal to 0 or x square plus 4 is equal to 0 but x is not equal to 0 therefore x square plus 4 is equal to 0 this implies that x square equals to minus 4 which is not possible because x is a real number hence xq plus 4x is not equal to 0 if x is not equal to 0 which is same as saying that q is not true implies that p dash is not true therefore from the key idea we can say that statement p is true. So this was what we were supposed to prove in this question I hope that you understood the question and enjoyed the session have a good day.