 Hello and welcome to the session. Let us discuss the following question. It says, write the contra-positive and converse of the following statements. Let us first learn the concept of the contra-positive and the converse statements. The contra-positive of the statement, if p then q is if not q then not p. That is if we are given a statement in the form if p then q then its contra-positive is given by if not q then not p. For example, I see a statement that if you get more than 85% you will get a price. So the contra-positive of the statement will be if you don't get more than 85% you will not get a price. So this is what we mean by the contra-positive. If not q then not p. And the converse of the statement if p then q is if q then p. Let us now see the first statement. It says if x is a prime number then x is odd. Now here we are given a statement in the form if p then q. Where p is the statement x is a prime number and q is the statement which says x is odd. Now we have to write the contra-positive of the statement. So the contra-positive is now we know that the contra-positive is of the form if not q then not p. So this is not an odd number then x is not a prime number. So we write the contra-positive of the statement if a number x is not odd not a prime number. Now we have to write the converse of the statement. That means we have to write the converse of the statement if x is prime then x is odd. And the converse of the statement is if q then p. So the converse will be if x is odd. Now the second statement is if the two lines are parallel then they do not intersect in the same plane. So we have to write the contra-positive of the statement where the statement p two lines are parallel and the statement q is the two lines do not intersect in the same plane and the contra-positive is given by if not q then not p. So statement q is the two lines do not intersect in the same plane. So not q will be the negative of the statement that is they intersect in the same plane right not p the lines are not parallel. So the contra-positive is intersect in the same plane they are not parallel. Now we have to write the converse of the statement that means we have to write the converse of the statement if p then q and its converse is given by if q then p. So here q is the two lines do not intersect in the same plane. So the converse is two lines do not intersect in the same plane then they are parallel. So this is the converse of the second statement. Let's now see the third statement it says something is cold implies that it has low temperature. That is the statement says if something is cold then it is at low temperature. We have to write the contra-positive. The contra-positive is if not q then not p. So if something is not at low temperature it is not cold right. So the contra-positive is if something is not at low temperature then it is not cold. Now we have to write the converse the converse of the statement if p then q is if q then p. Here the statement q is something is it is at the low temperature and statement p is something is cold. So if something is at low temperature then that thing is cold. So the converse is if something is at low temperature then it is cold. Now see the fourth statement it says you cannot comprehend geometry if you do not know how to reason deductively. Here the statement p is you cannot comprehend geometry and the statement q is you do not know how to reason deductively. And the state of the form if p then q has the contra-positive as if not q then not p. So the statement q is you do not know how to reason deductively. Not q means you know how to reason deductively and not p is you can comprehend geometry because p is you cannot comprehend geometry not p is you can comprehend the geometry. So the contra-positive is so the contra-positive is if you know how to reason deductively then you can comprehend the geometry. Now we have to write the converse of the statement and the converse of the statement if p then q is given by if q then p. So here q is this you do not know how to reason deductively and p is you cannot comprehend geometry. So the converse is if you do not know how to reason deductively then you cannot comprehend geometry. Let's now see the fifth statement it says x is an even number implies that x is divisible by four. So here the statement p is x is an even number and the statement q is x is divisible by four. So the contra-positive of the statement if p then q is given by if not q then not p. So if a number is not divisible by four then it is not an even number. This is the contra-positive. So the contra-positive of the statement if x is an even number then x is divisible by four is if x is not divisible by four then x is not an even number. Now we have to write the converse of the statement the converse of the statement if p then q is if q then p. So the converse of the statement is if this is divisible by four then x is an even number. This completes the question. Bye for now. Take care. Have a good day.