 Hello and welcome to the session. In this session we shall discuss how to use reasoning strategies to make conclusion from given statements of fact. There are two types of reasoning strategies. One is inductive reasoning and second is deductive reasoning. Now we are going to discuss inductive reasoning. In this type of reasoning we derive the conclusion after performing investigations, observing similarities and patterns and making generalizations. Let us consider an example. Consider the following sequence of numbers 2, 3, 5, 7, 11, 13 and so on. We say next number in this sequence will be 17 but how did we arrive at this conclusion? This conclusion is drawn by observing similarity between the numbers and the pattern formed by the numbers. We see that all these numbers do not have any positive divisor except one and itself. So we say that all these numbers are prime numbers starting from 2, next prime number is 3, then 5, then 7, then 11, then 13 and next prime number after 13 is 17 having two positive divisors that is one and itself. So next prime number in this sequence will be 17. Now we are going to learn about conjecture. It is an unproven statement which we do not know whether it is true or false. Let us consider an example. Verify the conjecture. Some of two even numbers is even that is we have to verify whether it is true or false to prove it we will use inductive reasoning. Now let us consider some specific cases where we will add any two even numbers. We take 2 plus 2 which is equal to 4 which is an even number. 12 plus 70 is equal to 82 which is again an even number. Now 220 plus 176 is equal to 396 which is an even number. 2,124 plus 3,256 is equal to 5,380 which is an even number. 11,552 plus 51,784 is equal to 63,336 which is also an even number. So we observe that some of any two even numbers is an even number. Thus using inductive reasoning the given conjecture is true that is some of two even numbers is even. Now we are going to discuss about deductive reasoning. In deductive reasoning a logical statement or argument is drawn by using facts, definitions and proven properties and facts. In simple words the conjecture given can be true or false and using deductive reasoning we will explain why it is true or false using known facts and properties. Let us consider the previous example only that is verify the conjecture some of two even numbers is even. Now we will verify this conjecture using deductive reasoning we know that even numbers are 2,4,6,8 and so on. We also know that even numbers are multiple of two. So any even number can be written as a multiple of two like 2n where n is a positive integral. Let us take any two even numbers say 2n and 2 into n plus 1 the whole. Now we find there is some and it is given by 2n plus 2 into n plus 1 the whole and it is equal to 2n plus 2 into n that is 2n plus 2 into 1 that is 2 so it is equal to 4n plus 2. Here we have used the distributive property which says a into b plus c the whole is equal to a into b plus a into c. Now taking two common from both these terms we get 2 into 2n plus 1 the whole c the sum 2 into 2n plus 1 the whole is again a multiple of two so it is also an even number. Thus using deductive reasoning we have verified some of two even numbers is even. This completes our session. Hope you enjoyed this session.