 I am Prof. R. V. R. Giddy from Computer Science and Engineering Department of Dublai Tishulapur. Today I will be focusing on principal consent to normal form, the various problem statements that we are going to solve as a part two. You will be able to convert the given equation into principal consent to normal form. Today's example, obtain the product of some canonical forms of the given formula for the following formula, the formula is P and Q and R and the second term is negation P and R and Q and the third term is negation P and negation Q and negation R. Now product of some canonical form is also nothing but a principal consent to normal form. Now the given formula is given formula, now if you observe the given formula, say the given formula, say name it as S and assume that this is equation number one. If you look at this particular formula, what we observe, it is a summation of three terms. Inside the bracket it is a product of variables with the negation. It means they are mean terms, mean terms are there and mean terms are taken into summation. This means the given formula is in the form of PDNF. The given formula is in the form of PDNF. Now we have to obtain PCNF, means that what we have to do, let us suppose this is equal to S. So the given formula is in P, S is a given PDNF, to obtain PCNF, to obtain PCNF. What we do? We take negation S, that negation S is nothing but principal dissent to normal form of the remaining mean terms. As we know that there are three mean terms, for three variables there are eight mean terms are there. So three are already consumed, three are already utilized in the PDNF. So remaining five mean terms are there, that we have to take in a summation, that we have to take in a summation, that will be called as a negation S. Now look at this, the mean terms are indicated over here, eight mean terms are there, M0 to M7, out of that I have mentioned in a red color that are used in a formula S, that is negation P and negation Q, that is the third term, negation P and Q and R, that is the second term and the third term is P and Q and R. So M0, M3 and M7 are used in a S or they are in the form of PDNF, they are in the form of PDNF. So it is a summation of what? M0, M3 and M7. So it is a principal descent in form of these particular three mean terms. Now negation S is equal to what? PDNF remaining mean terms means we have to take a summation of remaining mean terms are P, M1, that is M2, M3 is already in S, so M4 will come, M5 will come and M6 will come. Apart from this M0, M3, M7 remaining mean terms M1, M2, M4, M5 and M6 will come in the summation of remaining mean terms that is equal to say negation S. Let us write down this M1, M2, M4, M5 and M6 in a summation and that negation S. So this is S is equal to, negation S is equal to, it is already, so negation S is equal to here the actually formulas or the actually max terms, mean terms are written over here. So 1, 2, 3, 4 and 5 mean terms are written in equation number 2. So this is called as a negation S to obtain principal conjunctive normal form. We have to take negation of negation S, negation of negation S. So that will give us, so the remaining mean terms are this is M1, that is negation P and negation Q and R, it is written over here or negation P and Q and negation R, that is M2 is there. Then the third term is M5, P and negation Q and R and the fourth term is P and negation Q and R and fifth term is P and Q and negation R. So this all will come in a PDF, that is negation S, that is a summation of remaining mean terms. Let us go to the next slide, which we will focus on. So negation S is just repeated those statements over here in this slide and now find out negation of negation S, find out negation of negation S. Now this is nothing but, this is nothing but what we will do, negation of negation S is equal to, we will take negation then we will write the first mean term, okay that is negation P and negation Q and R, then R then we will write negation and this second mean term, okay, then R third mean term with a negation, R fourth mean term with a negation and R negation with a fifth mean term, say this is equation number 3, this is equation number 3. Now here we have to take this negation inside the bracket, okay, now see what will happen. If I take this negation inside the bracket, this will be using of course de Morgan's law. So negation of negation will go off, so it will remain simply P, it will be P R, so this and will change to R, okay and this and this negation will go off, this negation will go off, so it will remain as Q and this will become negation R, okay and this will be, R will be changed to and so this negation will go inside the bracket, okay, this negation will go inside the bracket, so what will happen, this negation will be applied to this negation P, so that will become P, this R will change to and this negation Q will be converted into negation Q and negation R will be converted to R, then R will change to and, so negation applied this negation to this third term, so this will be negation P or Q or this R will change and will change to R, okay, this R will change to R, this negation will be, R will become simply R and this R will become and and take this negation to the fifth term, so this will become negation P or Q or negation R rather this is fourth and fifth one is over here after converting this R to and, okay this negation will go into the bracket, so this will become negation P or negation Q or negation R, so this is what equation number three will be changing to equation number four after applying negation to the brackets, okay, so there as I have explained here it is P or Q or negation R, so this R and will change, R will change to and then the inside the bracket R and will change to R, so it will be P or negation Q or R, so wherever negation is there that negation will go off, if negation is not there negation will be applicable to that particular variable, okay, and the third term is this R will change to and, okay, negation will be applied to P, then this and will change to R inside the bracket, then Q was with negation, now when negation again one more negation will come it will become only Q and this negation R will become simply R and in the last mean term in the last mean term it is negation P or negation Q or R, this is equation number four, now think and write, okay, order the max terms for the equation number four, order the max terms for the equation number four, okay that equation number four was given here, what are the orders of these max terms, okay, take a pause over here and write down the order of these max terms on a piece of paper, so the answer for that is, for that answer is it is P or Q or negation R that is M1, okay, then M2, M2 will be there, then M4, M5 and M6, okay, so it is a product of M1, M2, M4 and M5 and M6, this is a required PCNF, this is a required PCNF, okay, so before that or in the previous, okay, so this equation number four, so this equation number four is a PCNF, this is a PCNF, okay, it is a principal conjunctive normal form. So let us go to the next slides that already we have, you have given the answer for this, these are the references and I hope you have understood how to convert the given any formula into a product of some canonical form or principal conjunctive normal form, thank you very much.