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Welcome to the next video. In[br]the Boolean series. In this

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video we will look at some[br]more examples of relatively

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simple trick tables.

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Now let's look at an[br]example, which is a slightly

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bit more difficult, not.

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P or Q.

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And are so in this case now I[br]have got three different inputs

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because I have got three[br]different letters, so the number

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of rows in my throught table[br]which is calculated by two to

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the N. In this case an the[br]number of inputs is 3, therefore

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this will be two to three, which[br]is 8. So I have got P.

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I have got Q and I have caught[br]R and the input combination half

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of eight is 4, so I'm going to[br]copy four trues an I'm going to

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copy for forces.

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Then I'm just going to copy[br]two truths, two forces

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until I finish filling the[br]table, and then in the last

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column I'm just going to do[br]them, alternating 1 by 1.

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Now, in this case you can see[br]that I have got every different

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combinations and I'm not[br]repeating any one of them, so

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this is the starting of the[br]setup of the table. Now what are

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the intermediate steps before we[br]can actually find the final

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answer for the output? Now there[br]is a bracket and within the

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bracket I have got P or QP or Q[br]will have to be one. I need to

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calculate. But then there is[br]a node operation in front, so

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I going to have to apply that[br]to the output of P or Q and

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then at the end I'm going to[br]have to use.

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The end operation to combine[br]everything together so P or Q,

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I'm going to use this table. Now[br]what do I know about the OR

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the OR only returns force if[br]both of the inputs are force? So

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I'm going to run through the[br]table and find the only inputs

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when both of them are force.

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And the rest of them I can just[br]quickly fill in.

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By truth, I could have gone[br]through two or two, gives me

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through three or two, gives me[br]through, etc. But this one is a

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nice and easy shortcut to

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remember. What does the note do?

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Change three to force and change[br]forced to true so the top half

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up to here is true. So every one[br]of them will be force.

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And the bottom two forces which[br]get then will turn into truth.

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And then I have to do the final[br]combination of not P or Q&R. So

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which are the two that I need to[br]combine together? Here I need to

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use this input.

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And I need to use the R.

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And what do I know about the end[br]and is only true if both of them

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are true? So I'm going to go[br]through the Roseanne. I'm going

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to filter out. Do I have double[br]trues in here? I have one in

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here. And I haven't got it[br]anywhere else, so the rest of

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them will have to be filled in[br]with forces becausw.

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And it's only true if both of[br]the inputs are true. In any

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other cases, the end will be[br]force, so knowing this shortcuts

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can save you quite some time on[br]filling in the tables.

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And now let's look at the last[br]example for this video.

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P. If only if.

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Q and not R. So this is[br]a similar example to the

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previous one because PQ&R I've[br]again have got three different

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inputs, so P.

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Q.

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R.

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Due to the power three gives[br]me 8, so it's to start the

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through table of correctly.[br]I'm going to have to place

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than four truth four forces.

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Two truth 246.

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And then just alternating[br]them 1 by 1.

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Right set up starting, setup,[br]done correctly. Then what do I

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need to look at? I need to look[br]at my priorities.

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There is a bracket here and[br]inside the bracket that is Q and

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not R to be able to combine[br]together Q and not our first I

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need to know what the values are[br]for not R so that's what I need

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to calculate first. Once I've[br]got the values for not RI can

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calculate Q and not R.

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And once that's done, I can[br]combine P together with the Q

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and not R using the if and[br]only if operation.

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Let's get started. R is[br]here, So what is not R every

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true becomes false an every[br]force becomes true.

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So now which are the two columns[br]that I need to combine together

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to find Q and not RI need Q?

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And I need not R.

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So and operation the end only[br]returns true if both of the

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inputs are true. So I'm going to[br]try to filter those ones out.

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And the rest of them I'm going[br]to fill in with force. Now, if

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you are not using lined paper,[br]then you want to be very careful

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about making sure that you[br]lining these trees and force

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values relatively easy to see,[br]because if you are getting a

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little bit wonky then you might[br]take a force for the upper or

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lower row instead of the road[br]that it belongs to. So be

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careful with that. Now I've got[br]Q and not R.

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But what I need here now is the[br]if and only if table.

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Remember if and only if it's[br]true. If the two input values

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are exactly the same and it's[br]false if the input values are

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different. So which columns am[br]I going to use here? But I

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need to use P.

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And I need to use the Q and not[br]R, which we just calculated

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here. So if they are the same,[br]I'm going to return true. If

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they are the different, I'm[br]going to return force. So look

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at this through force different.[br]So I'm returning a force true

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through the same. I'm returning[br]a true true enforce different.

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I'm returning a horse through[br]unforced, different returning or

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force force and force the same.

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I'm returning a tree 4th century[br]different. I'm returning a

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force. Force and force the[br]same. I'm returning a true and

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force on force the same.[br]Again, I'm returning the true.

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I hope you are gaining[br]confidence in finding solutions

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to trig tables now in the next[br]couple of videos we will look at

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some more difficult examples.[br]However, now it's your turn to

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do some practice questions. The[br]answers are at the end.

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So these are the practice[br]questions.

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And here are the answers.