 Hello and welcome to the session. In this session, first we will discuss statements. The basic unit involved in mathematical reasoning is a mathematical statement. A sentence is called a mathematically acceptable statement if it is either true or false but not both. We usually denote statements by small letters like p, q, r, etc. Consider the sentence, the earth is round. This sentence is true, hence it is a statement. Let us denote the statement by the letter p. Next we discuss negation of a statement. Basically, denial of a statement is called the negation of the statement. Like if we have p is a statement, then the negation of p is also a statement and is denoted by this, that is, it is read as not p. While forming the negation of a statement, we use phrases like it is not the case or it is false that, like if we have a statement p which says chinnai is the capital of Tamil Nadu, then negation of this statement is it is false that chinnai is the capital of Tamil Nadu or this could also be written as chinnai is not the capital of Tamil Nadu. So this is how we write the negation of a given statement. Next we have compound statements. Many mathematical statements are obtained by combining one or more sentences using some connecting words like and or etc. So we have a compound statement is a statement which is made up of two or more statements and in this case each statement is called a component statement. Like the statement which says number three is prime or it is odd. This is a compound statement which is made up of two statements given by q which says number three is prime and another statement given by r which says number three is odd. So these two are the component statements of the given compound statement. Now we shall discuss connectives like the word add which is a connecting word used in the compound statement. Let us now understand the role of the word add in the compound statement. The compound statement with the connective and in it is true if all its component statements are true and a compound statement with the connective and used in it is false if any of its component statement is false. This includes the case that some of its component statements are false or all of its component statements are false. Consider the compound statement given by p which says 4 plus 3 equal to 7 and 6 greater than 7. Now the component statements of this compound statement given by q 4 plus 3 equal to 7 and the other component statement given by r is 6 greater than 7. Here the statement q that is one component statement is true and the other component statement r is false. So as one statement is true and the other statement is false so the compound statement given by p would be false. Now let us discuss the other connective which is the word or. This is also used in the compound statement. Consider the statement to apply for a driving license. You should have a Russian card or a passport. The connective that we use here is or. Here the or that we are using is the inclusive or since a person can have both a Russian card and a passport to apply for a driving license. So in this case the or that we are using is called inclusive or. Consider the statement which says sun rises or moon sets. The connective that we have used here is or. Now this or is called exclusive or since in this case it is not possible that sun rises and moon sets together. So the or that we have used here is called the exclusive or. A compound statement with the connective or used in it is true if one component statement is true or both the component statements are true and the compound statement with the connective or used in it would be false if both the component statements are false. Consider the compound statement given by p which says 5 less than 7 or 8 greater than 10. Now the component statements are given by q at the first component statement be 5 less than 7 and the component statement are 8 greater than 10. Now the component statement q is true and the component statement are is false. So the compound statement p would be true since one component statement is true. Next we discuss quantifiers. Quantifiers are phrases like there exists and for all consider the statement there exists a number which is equal to its square. The quantifier used here is there exists. Now consider another statement which says for every real number x x is less than x plus 1. The quantifier used here is for every or we can also say for all instead of for every it means the same. So we have seen that many mathematical statements contains some special words like connectives like and or and quantifiers like there exists and for all and we really need to know the meaning attached to them specially when we need to check the validity of different statements. This completes the session. Hope you have understood the concept of statements negation of a statement, compound statement, the connectives and the quantifiers.