WEBVTT 00:00:18.180 --> 00:00:22.415 Welcome to the next video. In the Boolean series. In this 00:00:22.415 --> 00:00:26.265 video we will look at some more examples of relatively 00:00:26.265 --> 00:00:27.420 simple trick tables. 00:00:28.840 --> 00:00:33.140 Now let's look at an example, which is a slightly 00:00:33.140 --> 00:00:34.860 bit more difficult, not. 00:00:36.590 --> 00:00:38.030 P or Q. 00:00:39.320 --> 00:00:45.248 And are so in this case now I have got three different inputs 00:00:45.248 --> 00:00:49.808 because I have got three different letters, so the number 00:00:49.808 --> 00:00:55.280 of rows in my throught table which is calculated by two to 00:00:55.280 --> 00:01:01.717 the N. In this case an the number of inputs is 3, therefore 00:01:01.717 --> 00:01:07.835 this will be two to three, which is 8. So I have got P. 00:01:08.870 --> 00:01:15.464 I have got Q and I have caught R and the input combination half 00:01:15.464 --> 00:01:22.529 of eight is 4, so I'm going to copy four trues an I'm going to 00:01:22.529 --> 00:01:23.942 copy for forces. 00:01:25.670 --> 00:01:29.990 Then I'm just going to copy two truths, two forces 00:01:29.990 --> 00:01:34.742 until I finish filling the table, and then in the last 00:01:34.742 --> 00:01:39.494 column I'm just going to do them, alternating 1 by 1. 00:01:42.640 --> 00:01:47.346 Now, in this case you can see that I have got every different 00:01:47.346 --> 00:01:50.966 combinations and I'm not repeating any one of them, so 00:01:50.966 --> 00:01:55.672 this is the starting of the setup of the table. Now what are 00:01:55.672 --> 00:01:59.292 the intermediate steps before we can actually find the final 00:01:59.292 --> 00:02:03.636 answer for the output? Now there is a bracket and within the 00:02:03.636 --> 00:02:09.790 bracket I have got P or QP or Q will have to be one. I need to 00:02:09.790 --> 00:02:14.210 calculate. But then there is a node operation in front, so 00:02:14.210 --> 00:02:19.130 I going to have to apply that to the output of P or Q and 00:02:19.130 --> 00:02:22.410 then at the end I'm going to have to use. 00:02:24.850 --> 00:02:30.812 The end operation to combine everything together so P or Q, 00:02:30.812 --> 00:02:38.400 I'm going to use this table. Now what do I know about the OR 00:02:38.400 --> 00:02:45.446 the OR only returns force if both of the inputs are force? So 00:02:45.446 --> 00:02:51.950 I'm going to run through the table and find the only inputs 00:02:51.950 --> 00:02:55.202 when both of them are force. 00:02:55.530 --> 00:02:59.490 And the rest of them I can just quickly fill in. 00:03:00.280 --> 00:03:04.336 By truth, I could have gone through two or two, gives me 00:03:04.336 --> 00:03:08.730 through three or two, gives me through, etc. But this one is a 00:03:08.730 --> 00:03:10.420 nice and easy shortcut to 00:03:10.420 --> 00:03:12.970 remember. What does the note do? 00:03:13.980 --> 00:03:18.803 Change three to force and change forced to true so the top half 00:03:18.803 --> 00:03:23.626 up to here is true. So every one of them will be force. 00:03:27.100 --> 00:03:32.212 And the bottom two forces which get then will turn into truth. 00:03:32.212 --> 00:03:38.602 And then I have to do the final combination of not P or Q&R. So 00:03:38.602 --> 00:03:44.566 which are the two that I need to combine together? Here I need to 00:03:44.566 --> 00:03:45.844 use this input. 00:03:47.360 --> 00:03:49.488 And I need to use the R. 00:03:50.830 --> 00:03:56.926 And what do I know about the end and is only true if both of them 00:03:56.926 --> 00:04:01.498 are true? So I'm going to go through the Roseanne. I'm going 00:04:01.498 --> 00:04:06.832 to filter out. Do I have double trues in here? I have one in 00:04:06.832 --> 00:04:12.311 here. And I haven't got it anywhere else, so the rest of 00:04:12.311 --> 00:04:16.321 them will have to be filled in with forces becausw. 00:04:17.120 --> 00:04:22.450 And it's only true if both of the inputs are true. In any 00:04:22.450 --> 00:04:26.960 other cases, the end will be force, so knowing this shortcuts 00:04:26.960 --> 00:04:31.470 can save you quite some time on filling in the tables. 00:04:32.880 --> 00:04:37.148 And now let's look at the last example for this video. 00:04:38.610 --> 00:04:41.878 P. If only if. 00:04:43.030 --> 00:04:49.786 Q and not R. So this is a similar example to the 00:04:49.786 --> 00:04:55.416 previous one because PQ&R I've again have got three different 00:04:55.416 --> 00:04:57.105 inputs, so P. 00:04:59.260 --> 00:04:59.930 Q. 00:05:01.650 --> 00:05:02.100 R. 00:05:06.050 --> 00:05:11.055 Due to the power three gives me 8, so it's to start the 00:05:11.055 --> 00:05:14.905 through table of correctly. I'm going to have to place 00:05:14.905 --> 00:05:16.830 than four truth four forces. 00:05:19.000 --> 00:05:22.219 Two truth 246. 00:05:24.890 --> 00:05:27.634 And then just alternating them 1 by 1. 00:05:31.830 --> 00:05:35.515 Right set up starting, setup, done correctly. Then what do I 00:05:35.515 --> 00:05:39.200 need to look at? I need to look at my priorities. 00:05:40.030 --> 00:05:44.385 There is a bracket here and inside the bracket that is Q and 00:05:44.385 --> 00:05:49.075 not R to be able to combine together Q and not our first I 00:05:49.075 --> 00:05:54.100 need to know what the values are for not R so that's what I need 00:05:54.100 --> 00:05:58.120 to calculate first. Once I've got the values for not RI can 00:05:58.120 --> 00:05:59.795 calculate Q and not R. 00:06:01.700 --> 00:06:06.860 And once that's done, I can combine P together with the Q 00:06:06.860 --> 00:06:11.160 and not R using the if and only if operation. 00:06:12.200 --> 00:06:17.528 Let's get started. R is here, So what is not R every 00:06:17.528 --> 00:06:21.080 true becomes false an every force becomes true. 00:06:25.040 --> 00:06:29.967 So now which are the two columns that I need to combine together 00:06:29.967 --> 00:06:32.999 to find Q and not RI need Q? 00:06:34.670 --> 00:06:36.210 And I need not R. 00:06:37.470 --> 00:06:42.462 So and operation the end only returns true if both of the 00:06:42.462 --> 00:06:47.870 inputs are true. So I'm going to try to filter those ones out. 00:06:53.540 --> 00:06:58.314 And the rest of them I'm going to fill in with force. Now, if 00:06:58.314 --> 00:07:02.747 you are not using lined paper, then you want to be very careful 00:07:02.747 --> 00:07:06.157 about making sure that you lining these trees and force 00:07:06.157 --> 00:07:09.908 values relatively easy to see, because if you are getting a 00:07:09.908 --> 00:07:14.341 little bit wonky then you might take a force for the upper or 00:07:14.341 --> 00:07:18.433 lower row instead of the road that it belongs to. So be 00:07:18.433 --> 00:07:21.843 careful with that. Now I've got Q and not R. 00:07:22.100 --> 00:07:27.235 But what I need here now is the if and only if table. 00:07:28.090 --> 00:07:32.602 Remember if and only if it's true. If the two input values 00:07:32.602 --> 00:07:37.114 are exactly the same and it's false if the input values are 00:07:37.114 --> 00:07:41.626 different. So which columns am I going to use here? But I 00:07:41.626 --> 00:07:43.130 need to use P. 00:07:45.310 --> 00:07:50.910 And I need to use the Q and not R, which we just calculated 00:07:50.910 --> 00:07:56.110 here. So if they are the same, I'm going to return true. If 00:07:56.110 --> 00:08:00.510 they are the different, I'm going to return force. So look 00:08:00.510 --> 00:08:04.910 at this through force different. So I'm returning a force true 00:08:04.910 --> 00:08:08.910 through the same. I'm returning a true true enforce different. 00:08:08.910 --> 00:08:12.510 I'm returning a horse through unforced, different returning or 00:08:12.510 --> 00:08:14.910 force force and force the same. 00:08:15.050 --> 00:08:19.790 I'm returning a tree 4th century different. I'm returning a 00:08:19.790 --> 00:08:24.420 force. Force and force the same. I'm returning a true and 00:08:24.420 --> 00:08:27.750 force on force the same. Again, I'm returning the true. 00:08:29.690 --> 00:08:33.110 I hope you are gaining confidence in finding solutions 00:08:33.110 --> 00:08:38.430 to trig tables now in the next couple of videos we will look at 00:08:38.430 --> 00:08:42.230 some more difficult examples. However, now it's your turn to 00:08:42.230 --> 00:08:46.030 do some practice questions. The answers are at the end. 00:08:46.850 --> 00:08:48.830 So these are the practice questions. 00:08:54.940 --> 00:08:56.480 And here are the answers.