 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that write inverse, converse and contra-positive of the given conditional statement. If a number ends in 0 or 5 then it is divisible by 5. Also write a symbolic notation. As we know if we negate both the hypothesis and the conclusion and rewrite it in if then form then the new statement form is called the inverse of the conditional statement. If we exchange the hypothesis and the conclusion in the if then statement then the new statement formed is called the converse of the conditional statement. If we negate both the hypothesis and the conclusion of the converse of the conditional statement and rewrite in the if then form then the new statement so formed is called the contra-positive of the conditional statement. With this key idea let us proceed with the solution. We are given the conditional statement if a number ends in 0 or 5 then it is divisible by 5. It is in if P then Q form that is we have P implies Q is if a number ends in 0 or 5 then it is divisible by 5. So here hypothesis denoted by P is a number ends in 0 or 5 and conclusion denoted by Q is it is divisible by 5. Now we will write the inverse, converse and contra-positive of the given conditional statement along with the symbolic notation. First we shall write the inverse of a conditional statement. For this we negate both the hypothesis and the conclusion and rewrite it in the if then form. It is denoted by not P implies not Q. So here not P implies not Q is if a number does not end in 0 or 5 then it is not divisible by 5. Now we shall write the converse of a conditional statement. To write the converse we exchange the hypothesis and the conclusion in the if then statement. We will rewrite the statement if P then Q in the form if Q then P. It is denoted by Q implies P. So here Q implies P is if a number is divisible by 5 then it ends in 0 or 5. Now lastly we shall find the contra-positive of a conditional statement. For this we negate both the hypothesis and the conclusion of the converse of the conditional statement and rewrite in the if then form. It is denoted by not Q implies not P. We have the following conditional statement. P implies Q is if a number ends in 0 or 5 then it is divisible by 5. The converse of this statement will be Q implies P which is if a number is divisible by 5 then it ends in 0 or 5. Now we will write its contra-positive. Not Q implies not P is if a number is not divisible by 5 then it does not end in 0 or 5. This is the required answer. With this we complete our session. Hope you enjoyed this session.