 There are learners. Today, I will take the Unit non-6 of the 2.semester philosophy that is logic 2, the unit name is formal proof of validity. రాడతి మువసిstarter నువా ను నిసి акку�ిినిాననువారానాతు,趣 వియ్యవిమి఍కిము Fortnite కిall! developers, in this unit, we will discuss the basic points. కార్ద్వళాటిలు Ρటన తోలితోటa, strategy for deduction. తృతత్ర్మఫిక్ రరిRay Rlaw న౻కల aseg�ర్౨మిక్ guaranteed తాఱలంనార Australia అసటిస్మాప్యాబడాతిష్లల అససంనిక మావలేబాదకాగిదాటాపే పత dietsదాకోచరేనంన doorway up భార్స వరంవార్త సియది మాయది ఆరిటి సివరంవి సివామారి సిమని బారిసి తరాయి సింవన సివాకసింటిటది. పరటర్లాటకా, ఆగెణింికాడాయి కంత్త్నీనికి, కరంత్త్ని ఆంత్త్మోన్, నెచారాాకి. త్ట్ణికి, మ్న్చెగ్ఏ, పబరికిట్నికిత్ట్లి. ప్రరి or what may be called the method of derivation by substitution. The method of deduction is applicable to those arguments which are valid. In this method, we simply construct a proof of their validity in order to construct a formal proof of their validity. We have to apply certain rules to the given premises and go on deducing consequences from them unless and until we get the original conclusion. Since in this method, we deduce conclusion from the original premises to get the original conclusion through the application of certain rules. Thereafter, this method is called the method of deduction. Dear learners, this deductive procedure is called formal because it relies on the valid argument forms to show as to how the conclusion can be deduced from the given set of premises. The valid argument forms are used as the logical rules to determine the consequences which can be validly inferred from the premises. Now, dear learners, you see what is formal proof of validity. A formal proof of validity for a given argument may be defined to be a sequence of statements each of which is either a premise of that argument or follows from preceding statements by an elementary valid argument and such that the last statement in the sequence is the conclusion of the argument whose validity is being proved. This definition is taken from I am copy book is symbolic logic. Dear learners, a substitution instance of an elementary argument forms that is you see, so now I have to use blackboard for your comprehension. Now, dear learners, you see in the blackboard a substitution instance of an elementary argument forms. Now you see, dear learners, this is an elementary valid argument form because it is a substitution instance of the elementary valid form modus ponens. So, it results from p implies q, p therefore q, dear learners. Now, you see by substituting f implies g for p and negation h for negation i for q. Therefore, it is that form of that even through modus ponens is not the specific form of that given argument. So, now you see, dear learners, this is if we have to take p and q for h value negation i, then this is p for f implies negation g. So, the result will be q. So, this is a formula from p implies q, p therefore q. Now, you see, dear learners, what is the strategy for deduction? Now, we have to learn this. The formal proof of validity of an argument can be constructed easily. The strategy for deduction will be as follows. Number one, for constructing the validity of an argument formulated in ordinary language, the statements of the argument will be symbolized by using the capital letters of the alphabet to bring out the logical form of the argument. Number two, this proof of validity will be started by stating and listing the given premises of the argument in one column. Number three, all the premises and the statements deduced from them must be numbered serially and must be put in an on column and the conclusion must be separated from the premises and it must be written to the right of the last premise separated by a slanting line with the symbol therefore which automatically marks of all the statements above it to be premises. So, number D, the statements that are deduced from the original premises by the application of rules must be put along with the given premises with justifications written beside them. The justification premise, the statement from which and the rule by which the statement in question is deduced is the second step. The statements that are deduced from the original premises by the application of rules are to be taken as premises and a deduction must continue until we get the original conclusion. Now, dear learners, now we take an argument and see how the formal proof of validity of the argument can be constructed. There are two types of rules in derivation rules that is rules of inference and rules of replacements. Rules of inference and rules of replacements are the two sets of rules for derivation for deducing the conclusion. Rules of inference are nothing but some valid argument forms whose validity is established by two tables. So, these rules are used in constructing formal proof of validity too. The following rules are the rules of inference. So, dear learners, in rules of inference we find the rules like modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, destructive dilemma, simplification and conjunction, addition and absorption. So, these rules of inference, dear learners, correspond to elementary argument forms, the validity of which is established easily by two tables. So, these rules also can be used to construct formal proof of validity for more complicated arguments. So, dear learners, we have seen, we have used blackboard in order to show how we have to draw the conclusion from the following pages. So, you see, in these complicated arguments, we have to use the rules of inference in order to draw the conclusion. So, you see, in case of complicated arguments, basically we use rules of inference in order to draw the validity of the arguments. So, dear learners, you have to know these ten rules of rules of inference. So, now derivation rules. Rules of inference are not regarded as sufficient for constructing the validity of many other arguments. So, additional rules are required in such cases. As it is known, here only true functional compound statements, that is concern us, hence if any part of a compound statement is replaced by any logical equivalent expression, to the part replaced the true value of the resulting statement is the same as that of the original statement. This is sometimes called the rules of replacement and sometimes the principle of externality. The rule of replacement is adopted as an additional principle of inference. So, dear learners, now you have to know some additional rules apart from the rules of inference. The rules of replacement consist only of logical equivalences. For example, one of rules of replacements is de Morgan's theorem, that is negation back at begin p dot q, that is, you see dear learners how rules of replacements are there. Now you see, we have to show the logical form of de Morgan's theorem. de Morgan's theorem. Now you see, the logical form of this rule is negation p dot q equivalence negation p val negation p. So, this is the rule of de Morgan's theorem of rules of replacements. That is, negation back at begin p dot q back at true is equivalence to negation p val negation q. So, dear learners, we can infer one from other since they are logically equivalent. Therefore, negation p dot q is equivalent to negation p val negation q. Now, you have to know also the rules of replacements. So, in rules of replacements we find the rules like de Morgan's theorem commutation association distribution double negation transposition material implication material equivalence exportation tautology. So, these are the rules of replacements. So, in case of deducing conclusion in formal proof of validity dear learners, you have to know both the rules that is rules of inference and rules of replacements. So, each of these rules discuss in rules of inference and rules of inference stated as equivalences only in cases of rules of replacement. That is, we use basically the same line that is equivalencing as the main connective. This indicates that we can infer the left hand side of the equivalent from the right hand side and finds versa. So, dear learners so this is all about the unit formal proof of validity. So, the basic points discussed in this unit are the method of deduction is a method of establishing the validity of arguments. The truth table method is inconvenient for testing the validity of arguments containing a large number of statements. So, a more convenient method for testing the validity of arguments is the method of deduction or what may be called the method of derivation by substitution. So, rules of inference and rules of replacement are the two sets of rules for derivation. By means of these rules like rules of inference and rules of replacement we can know what can be validity infer from a certain kind of premises. Dear learners, rules of inference work in one direction these are modus ponen, modus tollens, hypothetical syllogism, disjunctive syllogism, constructive dilemma, destructive dilemma, simplification, conjunction and addition. So, rules of inference are not sufficient, dear learners for proving the validity of many other arguments. Therefore, rules of replacements are required as additional principles in such cases. Dear learners, rules of replacements are you have to know that these rules are D. Morgan's theorem, commutation, association, distribution, double negation, transposition, material implication, material equivalence, exportation and tautology. Now, dear learners, rules of replacement is indicated by the symbol like equivalence. So, these are the basic points and dear learners, in order to know the concept like formal proof of validity in a comprehensive way you have to study these following books. These books are logic informal, written by Sandasa Kraborty and Armin Kopi that is a book is symbolic logic and Kohenan Kopi that is a book introduction to logic and handbook of logic written by Munji Arsi Munsi and in order to know the basic rules of inference and rules of replacements other basic concept of logic you have to read a book like modern logic written by Sandasa Kraborty hope dear learners you have to know about what is formal proof of deduction or what is formal proof of validity or derivation rules in this unit and you have to know also how to deduce the valid argument using these two types of rules like rules of inference and rules of replacement thank you dear learners