 Hello and welcome to the session. In this session we are going to discuss conditional and biconditional statements and we will also discuss the inverse, converse and contrapositive of conditional statements. Let us start with the definition of conditional statements. The statements which are written in if then form are called conditional statements. If p and q are two given statements, then conditional statement will be written in the form if p then q. A conditional statement has two parts, hypothesis and conclusion. The clause followed by if is called the hypothesis and the clause followed by then is called the conclusion. The conditional statement is denoted by or and is read as p implies q. For example, we have a statement, an angle whose measure is less than 90 degree is an acute angle. Let us rewrite this equation in the if then form if the measure of an angle is less than 90 degree then it is an acute angle. Here the hypothesis is the measure of an angle is less than 90 degree and the conclusion is it is an acute angle. Now let us find the truth value of the conditional statement. In the conditional statement if p then q, p is the hypothesis and q is the conclusion. So here if p is true and q is false then p implies q is false. If p is false q is true then p implies q is true. If p is true q is true then p implies q is also true and if p is false q is false then p implies q is also true. For a given conditional statement we can write its inverse, its converse and contra-positive. Let us now discuss inverse of a conditional statement. If we negate both the hypothesis and the conclusion and rewrite it in the if then form then the new statement formed is called the inverse of conditional statement. The inverse of a conditional statement is denoted by not p implies not q. Let us continue with the earlier example. If the measure of an angle is less than 90 degree then it is an acute angle. Now we will write its inverse. As we know to write the negation of a statement we use the word not so its inverse will be If the measure of an angle is not less than 90 degree then it is not an acute angle. Now let us discuss the converse of a 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. The converse of a conditional statement is denoted by q implies p. For example the converse of the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle is given by if an angle is acute then its measure is less than 90 degree. Now let us discuss the contra-positive of a 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. The contra-positive of a conditional statement is denoted by not q implies not p. We have the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle. The converse of this conditional statement is if an angle is acute then its measure will be less than 90 degree. So its contra-positive will be if an angle is not acute then its measure will not be less than 90 degree. Now we come to biconditional statements. A biconditional statement is formed by joining the conditional statement and its converse using words if and only if. It is a conjunction of conditional statement p implies q and its converse q implies p so it is denoted by p implies q and q implies p or we can simply write it as this or this which is read as p if and only if q. We have the conditional statement if the measure of an angle is less than 90 degree then it is an acute angle. Its converse is if an angle is acute then its measure will be less than 90 degree. Now we write the biconditional statement using if and only if. An angle is an acute angle if and only if its measure is less than 90 degree. If both conditional and converse statements are true then the biconditional statement is also true. So the biconditional statement an angle is an acute angle if and only if its measure is less than 90 degree is a true statement. With this we complete our session. Hope you enjoyed the session.