 you have to see the blackboard. So I have to see, I have to write, I have to show some circles how logicians have used the Venn diagram technique for testing syllogism. They are learners. Now you see the section that is Venn diagram technique for testing syllogism. Now you see the learners. This section, the term Venn diagram technique to diagram the standard form categorical propositions. In order to diagram the standard form of categorical syllogism, it is necessary to take three circles for the term, for the three terms that is major term, middle term, middle term. This circle abbreviated as SPM. So you see the learners, you take the three circles. Now you see the three circles. So three circles abbreviated as SP, representing the, you see the minor term, the major term and middle term, middle term are drawn in such a way that they overlap each other. They overlap each other. So you see they are learners. We first draw the two overlapping circles. That is the circle S and the circle P. And then we draw the third circle M. This one M, this one M. So you see they are learners. The diagram of three overlapping circles mean S, P and M. Give the diagram of A plus. They are SPM as SP bar M bar, then S bar P M bar, then S bar P bar. Now they are learners. Now you see this diagram can be interpreted in terms of various classes. For example, we can take the lever S for the class of all scientists. This S indicates that all scientists. That P for that class of all philosophers. So this P indicates all philosophers. This indicates all philosophers. And first one that S indicates all scientists. This indicates all scientists. And M for that class of all mathematicians. So this indicates mathematicians class. Now they are learners you see. Now the part S, P bar M bar in this diagram represents the class of all scientists who are neither philosophers nor mathematicians. Again I repeat. So they are learners you see. S bar S, P bar M bar represents the class. So all are scientists who are neither philosophers nor mathematicians. So it is the product of three class scientists and non-philosophers and non-mathematicians. Now you see SP M bar is the product of the class scientists and philosophers and non-mathematicians. Now you see they are learners. You see SP M bar means what? That this is also the product of the class scientists and philosophers and non-mathematicians. Now they are learners you see. SP S, P bar is the class which is the product of scientists and mathematicians and philosophers. Which is the product of scientists and mathematicians and philosophers. The part SP M this part you see they are learners. So second one you see S bar P M bar means P means you see the all philosophers then it is non-scientists or non-mathematicians. This is also the product of the three classes. The three classes are that is scientists, philosophers and mathematicians. So first one you see that is philosophers who are neither scientists nor mathematicians. Now you see SP M means what? So this part SP M represents the class of all those people who are scientists and at the same time philosophers and mathematicians. This SP M so this means so all are scientists, philosophers and at the same time mathematicians. Now you see S bar S P bar M. So you see this also represents the three classes but you see so the classes are that scientists. All are scientists but they are not philosophers but they are mathematicians. Now you see S bar P M. So this also represents the three classes. The first one is scientists, the second one is philosophers then mathematicians. So you see this class represents that all are philosophers, mathematicians but they are not scientists. Here you see S bar P bar M this also represents the three classes but this says that this indicates that they are neither scientists nor philosophers but they are mathematicians. Now you see their learners so SP bar M bar. So this also represents the three classes but it indicates that this indicates that only the scientists but they are not philosophers and they are not mathematicians. So you see their learners it is the class of all those people who are neither scientists nor philosophers nor mathematicians SP bar M bar. So this indicates S bar P bar M bar it indicates that they are neither scientists nor philosophers nor mathematicians. So you see their learners by setting out or by inserting an X we can draw a diagram of any standard from categorical propositions whose terms are SP M. Now you see their learners by setting out or by inserting an X we can diagram any standard from categorical propositions whose terms are SP M. For example to diagram the proposition all S are P, SP bar 0 is equal to 0 we have to set out of all S that is not contained in P as shown below. You see their learners you see in the blackboard this is the first circle and second one is the another circle you see here we have to set this part you see so this is all S is P. So we have to set out of all out all of S that is not contained in P so you see we have to set this part which is not contained in P as shown in below you have to see the diagram. To diagram the proposition some S are P, S bar SP is not equal to 0 we have to put X in the overlapping part of the circle S and P. Now you see some S are P M here we have to write X means it indicates that to diagram the proposition some S are P SP is not equal to 0 SP is not equal to 0 means it indicates that there are some members here. So you see we have to put an X here we have to put X here in the overlapping part of the circle S and P here we have to write S some S are P SP is not equal to 0 here we have to write SP is equal to P bar is equal to 0. So you see the general technique of using Venn diagram for testing syllogism or for testing the validity of syllogism any standard form of categorical syllogism we have to follow some rules here that is in standard form categorical syllogism. So the reason we have three terms represented by S you see there are three circles here it indicates that there are three classes first one is S we indicate that scientists class then philosophers class then mathematicians class here there are three classes SP M. So it represents three terms so three circles represents three terms that is SP M first we draw the overlapping circles and they are level as S and P. You see the circle S stands for the minor terms so this stands for minor terms S and P stands for major term and you see and M stands for the middle term this one is middle. We diagram both the premises if one premise is universal and the other premise is particular then it is necessary to diagram the universal premise first and then to diagram the particular premise. So you see first we have to diagram the major premise then one is the minor premise then the conclusion here. It is to be noted that we need not diagram the conclusion rather we must respect the diagram to see whether or not the diagram of the premises contains in it the diagram of the conclusion. Again I repeat there are learners you see we diagram both the premises if one premise is universal and the other premise is particular then it is necessary to diagram the universal premise first and then to diagram the particular premise. Now you see there are learners the third point very important point that is it is to be noted that we not need not diagram the conclusion rather we must inspect the diagram means we must examine the diagram to see whether or not the diagram of the premises contains in the diagrams of the conclusion. If the diagram of the premises contains the diagram of the conclusion then there is given syllogism or a taken syllogism for testing that it is valid. If it is does not then if it is does not means if the diagram does not show the conclusion is contained in the circle then the syllogism will be invalid. So there are learners you see the diagram of the premises of a very document should be sufficient enough to include the diagram of the conclusion such that no further marking of the circles is needed. Now there are learners you see how we test the validity of the syllogism. Now you see there are learners you take an example all mathematicians are all mathematicians are philosophers. Second one you take all scientist are all scientist are mathematicians third one you take all scientist are philosophers all scientist are philosophers. Now you see there are learners this is an example of syllogism and how we have to test this syllogism using the hand diagram technique. You see there are learners this syllogism consists of a proposition all are a proposition you see a and a these are all a propositions see there are learners we have to draw the figures. Now you see the first one here we have to set this part m p by equal to 0 the first figure. The second one you see m by is equal to 0 we have to set this part this part and third one s m the third one you see you see s p m s p m here we have to set this part. So these three figures you see there are learners. Now you see figure one you see figure one represents the diagram of the premises m p by 0 m p m p by consist of two classes that is m p by r by m p by r. r by r m p s by that is not r that is m p by s by m m s p by these two parts are set in horizontally to indicate that m p by m p by 0. Likewise figure two represents the diagram of the premises s m by 0 here you see s m by consist of two parts that is s p by s p by or m by m s p by r. s p m by so these two parts are horizontally set it to represent the diagram of the premises like s m by 0. The conclusion of the syllogism s p by 0 demands that the parts here you see the third figure this is first one this is second one this is third one. Here you see the parts s s p by m and s m p by must be set it s s p by equal to 0. So the diagram of the two premises contain in them here you see the diagram of the two premises contain in them the diagram of the premises. Therefore the given syllogism that given syllogism you see all mathematicians are scientists all mathematicians are philosophers all scientists are mathematicians therefore all scientists are philosophers. So this syllogism is valid so they are liners in this way logicians have used the van diagram technique for testing syllogism whether the syllogism is valid or invalid. So in this way logicians have given forward that concept like hand diagram technique for testing syllogism. They are liners now you see the very basic points or highlighting points included in this unit there you see a standard form categorical syllogism consists of standard form categorical propositions. Second one the form of a standard form categorical syllogism is determined by its mood and figure which already have been discussed. The third one to test the validity of standard form categorical syllogism three overlapping circles are drawn we diagram both the premises but not the conclusion. The diagram of the premises must entail in it the diagram of the conclusion an argument is valid if and only if the diagram of the conclusion follow from the diagram of the premises. So they are liners these are the three basic points included in this unit. Now they are liners to know in details about this unit you have to consult some important books. These books are here you see you can take the book symbolic logic written by M. Gopi. And second one you can take another very important book that is written by Siam Kishore Singh book is modern logic. And also you can take another very important book that is written by Krishna Jain that is a text book logic. So they are liners I think you have benefited after going through this unique line standard form.