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For the given logic diagram write the Boolean expression: F(AB,C)B...

Question

For the given logic diagram write the Boolean expression: F(AB,C)B

For the given logic diagram write the Boolean expression: F(AB,C) B



Answers

Boolean Expressions

Given a conditional statement like this, A equals B means that the absolute value of a equals the absolute value of B. We can determine if we can make a by conditional statement using the same statements. P and Q. We do this by checking if he implies Q is true. And if Q implies P is true, we can tell clearly that P implies. Q. If a equals B and certainly the absolute value of a equals the absolute value of B. However, when we look at the converse of the statement, Hugh implies P we can think the absolute value of a equals the absolute value of B. This does not necessarily mean that a equals B. You can chew this by giving a counter example. Uh, my counter example that I think of is if a equals one d equals negative one, the absolute value of a is one and the absolute value of B is one so absolute value of a equals, the absolute value of B. But a does not eat will be. So we found a counter example that proves that our converse is false. So cute does not imply p because they're converses false. We can't write a by conditional statement from this conditional state

Uh so two triangles are given triangle abc and triangle X. Y. Zed. Uh First option we have to prove, we have to check whether this statement is true or not. A B. Uh let's check this, A B A B is going to be 12 and X. Y is going to be three. So this comes out to be four and Bc upon exit which is equal to B. C. Is given to the 16 and exit is given to B. Five which is not equal to four. Therefore maybe upon ex wife is not equal to B. C upon exit. So first statement is false. Now moving to the second segment. In second set when it is as uh in second segment it is asked to find B. C upon it to brew Bc upon A C. Is whether this is equals to X. Exert. Sorry, visor upon zero or not, lets again check this. So Bc upon a C is equal to B C. Is 16 upon a C. NBC is 16 upon a C. Is 20. So this comes out to be four upon five. This comes out before upon five. And uh eggs advisor upon exit is which is equals to wise, it is four and exit is five. So this is equals to Bc upon is hence the second statement is true And the second statement is true. Now moving to the 3rd statement After treatment, we have to uh inter treatment see now from the diagram we can see that this this side, the triangle abc triangle abc Triangle ABC is four times the tangle X, Y. Z. The sites of the four times around. For example, here X. Y. Z. X, Y. Z Land exercise three and here Abby's Well there is 3 to 4 and three into four. I'll get 12. Similarly four into four, I'll get 16 and similarly five into four. I'll get 20. That means triangle abc. That means strangle abc is similar to triangle X. Y. Z. Now, since triangle abc similar to triangle X. Y. Z. Then I can write then I can write these angles. These angles will also be this angle will also be similar. So I can write that is angle E. Is similar to angle X. And the angle B. Is similar to angle why And Angle C is similar to Angle zero. So our option So our option angle be similar dangled by an angle is in there. Doing the legs are also correct. So the final answer would be final answer would be A B C. D. Final answer would be B option B, C N. D. Final answer would be option B, option C and D. Because we have to mark it is a multiple choice question. We have to mark all the true statement So answer would be B C N B. Hope you understand the solution

Hello Gabe's today. We have some questions and we need to verify that each one of them is a pathology. So let's start with the first one. Uh P. And Q. Implement P. So that we know have P implies Q. This logical equivalent to negation P. Or Q. So we're gonna use this identity too much. And that's the problem. So let's start um P. And Q implement P. This logically equivalent to negation he and killed or he and according to the emergency law, this equivalent to a negation P. Or engage in Q. Or pete. So if we can collect negation B. With B. Uh This equivalent to negation pete or P. and one bracket for negation Q. And this equivalent this is a covenant tool. True all the time or negation Q. And this is logical equivalent to true. Which is the definition of the torch to the next port or the next problem. We have P implement P. Or cube. So this is logical equivalent to negation P. Or P. Or Q. Okay so here we can say that engage M. P. Or P. And one crack it according to the distributive law or kill. And this is the same as the one above is true or Q equals true. This is the definition of pathology to so and the next problem is negation P. Implement P. Implement Cube. And this is in one packet. This logical equivalent to negation negation P. Or P implement Q. Okay guys so and we know that negation negation P is the same as P. Or negation P. Or cute. And this again P or negation P. Or Q. And it's equivalent two pathology or cure equal the dutch. And again the first problem we have he and Q. And around packet implement P. Yeah, implement Q. So let's see that again here in the left hand side we have negation or so. Sorry, it's not like that. Um Okay again this is logically equivalent. Two negation P. And Q. Or he implement kill. This is logically equivalent to a negation P. Or negation Q. Here and here we have negation pete or cute. So here we have Q. Negation Q. Or Q. and one crack it four negation P. Or negation B. And that we know uh negation P. Or negation be as negation be itself and this is true or negation P. Which is true. Okay guys and uh let's story a new question which is the negation radiation P implement cube implement P. This equal it's this equals two negation negation P. Or pure implement P. Normally then we have according to the team organs though negation negation PSP itself and and negation cute. Okay this implements P. So we have here negation P. And negation Q. Or. Okay this is logically equivalent to negation P. Or cute. Yeah. Or Yeah. And here we have again P. Or negation P. Or Q. So we have here through always uh or cube which is again true. And the last one of the problem here is negation. He implements Q implements negation Q. Here we have negation navigation P. Or Q implements negation. Sure. Here we have B. And negation Q implements negation Kill. Here again we have negation P. And negation Q. Or negation Q. And the last stuff is according to the morgans. Do we have negation P. Or negation negation Q. Which is Q. Itself or negation Q. And here if we have the queue or or negative Q. Or negation Q. And one packet. So we have negation P. Or true, which is again and again and again. True. And that's it.

Sort of give given logic circuit is this now we will be solving this. So for your understanding, let me clarify this that Mhm. So this symbol is for this symbol is for and get the symbol is for not get and the symbol is for all right again. So starting with so starting from Mhm. So starting from this here here P is over here so and here here it is P. Here it is Q. So they are passing through the and gate so that all put away here would be P. Into cubes. So these are the ways to represent and uh represented logic. So in and get uh they could get multiplied or you can say they put they could get multiplied. This is uh this is to understand that it's not like they actually multiplied but the answer the output comes out to be multiplication of that. That means if he either any one of them is zero then this is real. So after and get the P. N. Q. Inputs after and get it get very pendant by PQ. Similarly here we are having pizza and here it is passing through nan get so here it is Q. So after passing through Nangle did get into a reward of that that is cuba. We represent that by cuba and it uh both this input a passing through and did so again we're here in cuba, Cuban means oppose it of you, that is inward of you here again this is uh this is inward of P. And this is in word of you and again passing through and get So this is a P back cuba. Now uh this uh now this and gate in this an alligator. The PQ and the P cuba of our father than input. So the output will be some of this. There is PQ plus B, cuba. So here the output is speaking to cuba and this output is input for the other input for the last year. Uh Last logic last get or get. And these two other this and these are the input for the lottery. These uh these other input. These two let it speak cuba and PQ plus P cuba are the input for the last two. Get organs. So the final are will be equal to PQ plus P cuba plus PBA cuba since it is or get. So the improve will get added. So now our final answer, our final logic gate that is uh the forces. The final boolean expression is this, there is PQ plus cuba plus Bba, cuba. Now we need to simplify the circuit. So uh to simplify circuit, R. Is equal to P. Q plus P Q. Bad plus pick back to back. Now first in these two terms are taking p common, so we are left taking the comments of the electorate, Q plus cuba and cuba cuba. We know that Q plus cuba. There is this is always true are always fun. This is all these two suppose if the true travel for support the trouble is 01 and for cuba it would be 10, then there's then there's some that is Q plus Q Plus cuba would be +1010101. It would be always true. Or you can say it would be always one. So this comes out with P plus P. Bar cuba. Now it gets simplified to P plus cuba. PBA. Now we can for mm. So the simplified was the simplified, the boolean expression comes out to be R. Is equal to P plus P bar cuba. Now we need to make a logic circuit out of this. So we can we can think of something like uh the first we can make uh there's an orbiting PNP cuba. So we can use our place so we can use an organ to make this and the second to get P cuba product of cuba. So first we need to we need to use uh not get to convert P two PBA and you to cuba. And after that we can after that weekend or this with something. Uh Okay, well this can be more simplified. This can be most important simplified by using by using distributed law by using distributive law that distributed lies something like uh support if there's A plus B into C. Then according to distribute the load, this can get an A plus B. A Plus B. Indu a policy. So similarly applying distributor on this. So this are can be written as be blessed be bad into people us cuba. So people people and people of cuba. Now uh for PNP ba bye complement property PNP but this is always one Oregon city is always true. So as more simplified uh billion expression comes out to be our x equals two P plus cuba. The most simplified within expression is this as your the people of cuba. So in order to get this uh first to to get plus in between so we need to use or and get invert that is cuBA. We need to use and not get so supposed I'm having a are over here you to my my my bring is bad just because this is an or gate uh so one input will be uh so let me begin with color. So green will be having R. P. Green is having P. And let's rip it. And okay so we need who A year we need a cuba. So we will be first using A. And sorry not get to convert you into cuba. So here P is away forcing buddhist P. And here you get converted from the not get it get promoted to the cuba. So and here it is or get so the art comes out that is output comes out to be P plus cuba. Here it is, here it is P and here it is cuba P in cuba and put the organs. So the and so the logic simplified logic would be this Rather than using such a big big, such a large amount of it can be simplified to this.


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