 cü సివార రారంగామాబానిలా మనిక౿నిరా రంటిష్రంగాపి మరో చాంటికెటా. ల్రికూటిటా నికిక్లి ఇఆఖ్త్టాపెయ. In this unit we will discuss the basic points there what is implication, different meanings of implication, features of implication, material implication. Now you see there learners the word implication has its reference in connection with deductive inference only. In this unit we shall be discussing a very important aspects of deductive inference that is implication. In other words the word implication has its reference to deductive inference. We will infer in our day to day lives logic develops and provides a system of metals and principles that may be used as a criteria for evaluating the inferences and guides in constructing correct inference and distinguishes them from incorrect ones. There learners implication is the logical relation that holds between the antecedent and the consequent of a conditional or hypothetical statement. I will repeat again implication is the logical relation that holds between the antecedent and consequent antecedent and consequent. Holds a relation between the antecedent and the consequent of a conditional or hypothetical statement. A conditional or hypothetical statement is a compound statement where two statements are joined by the word if before the first and inserting the word then between them. It means we use the two parts antecedent and consequent part by the word if then. So you see there learners such a hypothetical or conditional statement is also called an implication or an implicative statement. The relation of implication is the basis of a conditional or hypothetical proposition. When two simple statements are joined together by the connective if then, then the complex proposition obtained thereby is called a conditional or hypothetical proposition. In such a proposition the component statement that follows the if is called an antecedent part or the implication it is also called implication. And the component statement that follows the then is the consequent is the consequent or it is called as implicate. It is also called implicate. There learners if we can take here some examples to understand the relation between the two parts. First one is if and the second one is then or you can say it is implicate or implicate. There learners you take example if the rulers become corrupt then the common people become rebellious. You see I take the example if the common people become corrupt then the common people become rebellious. You see in this conditional proposition the portion the rulers become corrupt the rulers become corrupt here rulers become corrupt. This is the first part of the conditional proposition. You see the first part if the rulers become corrupt is so called as the antecedent part and the second part that then the common people become rebellious. This is the second part of this conditional proposition that is called as consequent part. You see there learners implication is the logical relation obtaining between the consequent and the antecedent by virtue of which the consequent follows from the antecedent. There learners implication is the most important relation obtaining between the premises and the conclusion of a deductive argument. A deductive argument is in fact a complex hypothetical statement which asserts that if the premises are true then the conclusion is also true. In a formal or deductive logic implication is very important. It is basis of a conditional or hypothetical statement because of which consequent follows from the antecedent. Similarly we can also say that the conclusion of a valid deductive argument follows necessarily because of the relation of implication. Such is the importance of implication in modern logic that the modern logic is sometimes called the logic of implication. Now there are learners, there are some questions are given for you. Suppose first question that is given as fill out the blanks. The word implication has its reference only with fill out the blanks inference. You write the correct answer. Second one is the relation of implication is the basis of a dash proposition. A deductive inference is based on the relation of dash obtaining between the constituent proposition. Again there learners you can give an example of implication and you write what is implication. There learners different meanings of implication. There are different types of implication as there are different hypothetical or conditional statements. In other words different hypothetical or conditional statement express different meanings of implications. Following are the different types of conditional statements each of which seems to assert different forms of implication. There learners you take some examples. You first one if all the students are studious and Raja is also a student then Raja is also studious. You take if all the students are studious and Raja is a student Raja is also a student then Raja is also studious. Second one you take if ABC is a triangle, if ABC is a triangle then the summation of its angles is equal to 180 degrees. Third one you take if this gold ring is placed in fire if this gold ring is on fire then it will become brighter then it will become brighter. Number four you take if you clean up your room if you clean up your room then I will buy you toy you want so there are learners these are the four examples of implication. Now you see in the first example the consequence part is the consequence you see if all the students are studious and Raja is also a student then Raja is also studious. You see in the first example the consequence part is logically deduced from the first one if all the students are studious so this is a decision part and the latter part is then Raja is also studious so the consequence part Raja is also studious is deduced logically deduced from the antecedent part so you see thus the example one explains the logical relationship between the antecedent and the consequence in the second case the consequence is deduced from the definition of the word in the antecedent part so you see example two conveys a definitional relationship by definition of a triangle the consequence follows the second example you see if ABC is a triangle then the summation of its angles is equal to 180 degrees so here this example gives us a definitional relationship because by the definition of a triangle the consequence follows the consequence means the summation of its angles is equal to 180 degrees so you see in a third case the consequence follows from its antecedent empirically it exhibits a causal connection based on experience you see the third one if this gold ring is in fire it will become brighter so this indicates a causal connection based on experience the aligners finally the fourth case the statement reports decision of the speaker to behave in the specified way under the specified circumstances it is a promise the fulfillment of which depends upon a certain behavior thus all the four conditional statements express different implications between the antecedent and the consequence therefore the word implication refers to our specific form these are first one is logical you can say second one you can say definitional and third one you can say causal and fourth one you can say decisional or behavioral decisional CISI ONL decisional or behavioral so these are the four forms of the relationship between the antecedent and the consequence the above four types of implication are different in that each asserted different type of implication between each antecedent and the consequence but they are not completely different all asserts types of implication between the antecedent and the consequence there is a common feature running through all these four forms of the relationship between the first part antecedent and the second part that is consequence it is that all these conditional statements will be false in a particular circumstances that is when the antecedent is true and the consequence is false a conditional statement is false when the antecedent is true and the consequence is false it means that we can show in such a way the aligners you see P, Q, P implies E if the antecedent part is true and also the consequence part is true then the whole function will be true again if the antecedent part is true and the consequence part is false than the whole function will be false if the antecedent part is false and the consequence part is true then the whole function will be a conditional statement to prove. Again if the consequence and decision part is false and the consequent function is also false, then the truth table of the conditional statement P implies Q, then that will be true. You see there is a common feature running to all these force forms, it is that all this conditional statement should be false in a particular circumstance that is when the antecedent is true and the consequent is false. You see a conditional statement is false when the antecedent is true and the consequent is false. This feature is the common partial meaning of implication, but it by itself does not express the complete or full meaning of implication. In order to express this common partial meaning of implication, the symbol implies horso or hook sign is used, this is called horso or hook sign. There are some characteristics of implication, so you see implication is a necessary relation when one proposition implies another proposition, the implied proposition is strictly determined by the first. In other words, if there is a relation of implication between P and Q, then the relation is such that if P then only and only Q. Second one is implication is a formal relation, this means it has no reference to material truth. This is the reason that implication holds in deductive inference only. The relation of implication is not concerned at all with the material truth of the proposition. These two pieces have distinguished implication from inference. Now we can see for example, A – No philosophers are fit for the country and some philosophers are precedent, therefore some presidents are not fit for the country. Second one is if no philosophers are fit for the country and some philosophers are precedents, then some philosophers are not fit for the country. నిిని పిసంటాతా మింరంతీన్చి, మిన్ట్చికకిస్ ఉచిన్చిమినింరంటరం మనే పికిసక్. berish  auc� opard তবীীীব গజ কజ স� wings কజ য఍রর এజ পরর্ রব ক఍রররর ক఍ররর কజ মরররর পরররর কజ মజ তజ বజ �彡ররর সূরর কజ তజ সূররর চజ কజ সূরররর কజ নূর�  descrição gere pa redef 那 are important in section here—the difference between implication and inference. implication, inference implication is a statement of logic To the effect that if certain conditions are fulfilled, then certain consequences will result, on the other hand in inferences the premise or the premises make certain assertions and as logical consequences of these assertions a further assertion is made namely the fact stated in the conclusion. So here you can take an example of inference there is a smoke there is a smoke in the hill and from this assertion we infer that there is fire in the hill so this is all about the every simple example of inference besides being formally true and inference must also be materially true on the other hand any implication can be asserted without prejudice to the question of the truth or falsity of the premises in other words formal truth is the sole concern of an implication it has nothing to do with the question of material truth when we make an inference we assume the truth of the premises and as a consequence of the truth of the premises and a logical validity of the argument we are entitled to a certain conclusion the statement if all humans are mortal and socrates is a human then socrates is mortal expresses implication the argument no man are perfect and some man are honest therefore some man are not perfect expresses inference their learners so this is all about the unit of inference and implication now you take the summary of this unit now you see their learners implication has different meanings we can distinguish different senses of implication that we are already discussed you see the logical relationship definitional relationship causal relationship and behavioral and decision and relationship between the antecedent and the consequent material implication is the type of implication which asserts that as a matter of fact it is not the case that the antecedent is true when the consequent is false the symbol for a material implication is the if then or also which is a truth functional connective like the symbols for conjunction and disjunctions as such it is defined by the truth table specific to it which I already shown to you there are some features of implication which distinguish it from inference implication is a purely necessary formal relationship the statement if all humans are mortal and socrates is a human then socrates is mortal express implication implication is a statement of a logic to a fact that if certain conditions are fulfilled then certain consequences will result it says nothing as to whether or not the condition referred to in the if clause are in fact fulfilled on the other hand in an inference the premise or the premises make certain assertions and as a logical consequences of these assertions a further assertion is made namely the fact stated in the conclusion now they are learners to understand or to comprehend this you need no five inference and implication you have to read some important books that book is introduction to logic written by copy arbing am copy and cohen and Carl another very important book you can to take logic written by modus on the sand and stan bernad their learners another very important book you can take logic informal symbolic and inductive written by sanda sacraborty another important book symbolic logic written by I am copy and another very very important book that is introduction to symbolic logic written by bason I think they are learners you have understood the unit five inference and implication and for understanding more you read the books which I refer to you thank you they are learners