 nınthereal foreigners, today we will teach you సోు�ACK క్ఫతి hence rules of replacements కిక్ 얼�Tr కోడ౜఍బ త౏ధ్రత్నని్యెట్చంకంగిరైMoon. కగüpగౌత౅లా,feit తచేన Loy acordoట్న. ancer down . రీవాథ౦ి Now dear learners, you see, what is rules of replacement? Dear learners, in the preceding two sectors, like formal proof of validity and rules of inference, you have already come to know the formal proof of validity, which discusses the concept life strategy for deduction, rules of inference including some solved examples of using these rules. Rules of replacement in a very brief manner, differences between rules of inference and rules of replacement, test of formal proof, general suggestion for formal deduction. However, dear unit, this unit will exclusively discuss the rules of replacement and also the application of the rules of replacements. Dear learners, you see, in rules of replacement, there are ten rules you will find, but there are many valid truth functional arguments whose validity we cannot prove by using only the nine rules of inference. As for example, in order to construct a formal proof of validity for the following problems, rules of inference are not enough. Now dear learners, you see, a implies b, c implies not b, therefore a implies not c. Dear learners, you see, to solve this kind of problem, some additional rules are required. With the help of these rules, we can replace any component of a statement by any other statement logically equivalent to the component replaced. For example, using the principle of double negation, which asserts that p is logically equivalent to double negation p. We infer from a implies double negation b, any of the following, you see, this one, a implies b, double negation a implies double negation b and also we can infer, you see, double negation back at begin a implies b or a implies four double negation b by rules of replacement to make the ten rules definite. We list ten totorojas logically through bioconditionals with which it can be used. These bioconditionals provide additional rules of inference to be used in providing the validity of argument. Dear learners, now you see, what are the rules of replacements. Now you see, in rules of replacements, we find the rules like de Morgan's theorem, commutation, association, distribution, double negation and transposition. So these are the rules of replacements. Now dear learners, you see, what is de Morgan's theorem. Now you see their learners. So negation p back at begin p.q equivalence, then back at begin negation p val negation q. Again you see their learners negation back at begin p val q equivalence back at begin negation p dot negation q. So this is nothing but the de Morgan's theorem. So dear learners, you see the another rule that is commutation, then association, then distribution, then double negation and transposition. So dear learners, you see another rules of replacements. They are material equivalence, material implication, material equivalence, exportation, tautology. So these are the rules of replacements. Now dear learners, you see how can we apply the rules of replacements in case of or in order to test the validity of argument. Now dear learners, you see some short examples for your understanding. It is given here. Now you see back at begin a implies b dot back at begin c implies d therefore a implies b dot negation d implies negation c. So how can we derive the conclusion out of the premise like a implies b dot c implies d. So you see dear learners, the argument or the conclusion that is a implies b dot negation d implies negation c. So this conclusion we derive from the premise one applying the rule transposition and in this way we can derive the conclusion a implies b dot negation d implies negation c. Now dear learners, you see the second one that is e implies f dot g implies negation h therefore negation e val f dot g implies negation h. So dear learners, you see how can we derive the conclusion out of the premise e implies f dot g implies negation h. Dear learners, we apply the rule equivalence in order to find out the conclusion negation e val f dot g implies negation h. So dear learners, we apply the rules of equivalence. Now dear learners, you see the last one that is x val y dot negation x val negation y therefore x val y dot negation x back a close val x val y dot negation y. Here dear learners, we apply the rule that is distribution in order to find out the conclusion out of the premise. So these are the some sold examples of the rules of replacement. Now dear learners, you see so what are the some basic points we discuss in the unit rules of replacements. Now dear learners, you see in order to construct formal proof of validity with rules of inference we need some other rules that is rules of replacements in order to find out a valid conclusion out of the premise. So you see in rules of replacement dear learners we find ten rules. So you see in the rules of replacement one side of the statement can be replaced with the other side of the equivalent statement. Already you have some examples, some sold examples of the rules of replacement. So dear learners, rules of replacement can be applied to a part of the statement two which is not possible in case of rules of inference because it says that or it implies that rules of inference is not sufficient in case of finding out or in order to test the validity of arguments and therefore rules of replacements are essential in order to find out the validity of arguments. Now dear learners, in order to know more of the rules of replacements or in order to know very in a comprehensive manner you have to read there are some good books, these books are you can take Sanda Sokrobot's book that is logic, informal, symbolic and deductive. You can take Irving Kopi's book that is symbolic logic. You also take Cohen and Kopi's introduction to logic and these are the following some books you have to take for consolidation in order to know more of this unit like rules of replacements. I think dear learners you have benefited to know about the rules of replacement that is unit number eight. Thank you.