1 00:00:18,180 --> 00:00:22,415 Welcome to the next video. In the Boolean series. In this 2 00:00:22,415 --> 00:00:26,265 video we will look at some more examples of relatively 3 00:00:26,265 --> 00:00:27,420 simple trick tables. 4 00:00:28,840 --> 00:00:33,140 Now let's look at an example, which is a slightly 5 00:00:33,140 --> 00:00:34,860 bit more difficult, not. 6 00:00:36,590 --> 00:00:38,030 P or Q. 7 00:00:39,320 --> 00:00:45,248 And are so in this case now I have got three different inputs 8 00:00:45,248 --> 00:00:49,808 because I have got three different letters, so the number 9 00:00:49,808 --> 00:00:55,280 of rows in my throught table which is calculated by two to 10 00:00:55,280 --> 00:01:01,717 the N. In this case an the number of inputs is 3, therefore 11 00:01:01,717 --> 00:01:07,835 this will be two to three, which is 8. So I have got P. 12 00:01:08,870 --> 00:01:15,464 I have got Q and I have caught R and the input combination half 13 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 14 00:01:22,529 --> 00:01:23,942 copy for forces. 15 00:01:25,670 --> 00:01:29,990 Then I'm just going to copy two truths, two forces 16 00:01:29,990 --> 00:01:34,742 until I finish filling the table, and then in the last 17 00:01:34,742 --> 00:01:39,494 column I'm just going to do them, alternating 1 by 1. 18 00:01:42,640 --> 00:01:47,346 Now, in this case you can see that I have got every different 19 00:01:47,346 --> 00:01:50,966 combinations and I'm not repeating any one of them, so 20 00:01:50,966 --> 00:01:55,672 this is the starting of the setup of the table. Now what are 21 00:01:55,672 --> 00:01:59,292 the intermediate steps before we can actually find the final 22 00:01:59,292 --> 00:02:03,636 answer for the output? Now there is a bracket and within the 23 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 24 00:02:09,790 --> 00:02:14,210 calculate. But then there is a node operation in front, so 25 00:02:14,210 --> 00:02:19,130 I going to have to apply that to the output of P or Q and 26 00:02:19,130 --> 00:02:22,410 then at the end I'm going to have to use. 27 00:02:24,850 --> 00:02:30,812 The end operation to combine everything together so P or Q, 28 00:02:30,812 --> 00:02:38,400 I'm going to use this table. Now what do I know about the OR 29 00:02:38,400 --> 00:02:45,446 the OR only returns force if both of the inputs are force? So 30 00:02:45,446 --> 00:02:51,950 I'm going to run through the table and find the only inputs 31 00:02:51,950 --> 00:02:55,202 when both of them are force. 32 00:02:55,530 --> 00:02:59,490 And the rest of them I can just quickly fill in. 33 00:03:00,280 --> 00:03:04,336 By truth, I could have gone through two or two, gives me 34 00:03:04,336 --> 00:03:08,730 through three or two, gives me through, etc. But this one is a 35 00:03:08,730 --> 00:03:10,420 nice and easy shortcut to 36 00:03:10,420 --> 00:03:12,970 remember. What does the note do? 37 00:03:13,980 --> 00:03:18,803 Change three to force and change forced to true so the top half 38 00:03:18,803 --> 00:03:23,626 up to here is true. So every one of them will be force. 39 00:03:27,100 --> 00:03:32,212 And the bottom two forces which get then will turn into truth. 40 00:03:32,212 --> 00:03:38,602 And then I have to do the final combination of not P or Q&R. So 41 00:03:38,602 --> 00:03:44,566 which are the two that I need to combine together? Here I need to 42 00:03:44,566 --> 00:03:45,844 use this input. 43 00:03:47,360 --> 00:03:49,488 And I need to use the R. 44 00:03:50,830 --> 00:03:56,926 And what do I know about the end and is only true if both of them 45 00:03:56,926 --> 00:04:01,498 are true? So I'm going to go through the Roseanne. I'm going 46 00:04:01,498 --> 00:04:06,832 to filter out. Do I have double trues in here? I have one in 47 00:04:06,832 --> 00:04:12,311 here. And I haven't got it anywhere else, so the rest of 48 00:04:12,311 --> 00:04:16,321 them will have to be filled in with forces becausw. 49 00:04:17,120 --> 00:04:22,450 And it's only true if both of the inputs are true. In any 50 00:04:22,450 --> 00:04:26,960 other cases, the end will be force, so knowing this shortcuts 51 00:04:26,960 --> 00:04:31,470 can save you quite some time on filling in the tables. 52 00:04:32,880 --> 00:04:37,148 And now let's look at the last example for this video. 53 00:04:38,610 --> 00:04:41,878 P. If only if. 54 00:04:43,030 --> 00:04:49,786 Q and not R. So this is a similar example to the 55 00:04:49,786 --> 00:04:55,416 previous one because PQ&R I've again have got three different 56 00:04:55,416 --> 00:04:57,105 inputs, so P. 57 00:04:59,260 --> 00:04:59,930 Q. 58 00:05:01,650 --> 00:05:02,100 R. 59 00:05:06,050 --> 00:05:11,055 Due to the power three gives me 8, so it's to start the 60 00:05:11,055 --> 00:05:14,905 through table of correctly. I'm going to have to place 61 00:05:14,905 --> 00:05:16,830 than four truth four forces. 62 00:05:19,000 --> 00:05:22,219 Two truth 246. 63 00:05:24,890 --> 00:05:27,634 And then just alternating them 1 by 1. 64 00:05:31,830 --> 00:05:35,515 Right set up starting, setup, done correctly. Then what do I 65 00:05:35,515 --> 00:05:39,200 need to look at? I need to look at my priorities. 66 00:05:40,030 --> 00:05:44,385 There is a bracket here and inside the bracket that is Q and 67 00:05:44,385 --> 00:05:49,075 not R to be able to combine together Q and not our first I 68 00:05:49,075 --> 00:05:54,100 need to know what the values are for not R so that's what I need 69 00:05:54,100 --> 00:05:58,120 to calculate first. Once I've got the values for not RI can 70 00:05:58,120 --> 00:05:59,795 calculate Q and not R. 71 00:06:01,700 --> 00:06:06,860 And once that's done, I can combine P together with the Q 72 00:06:06,860 --> 00:06:11,160 and not R using the if and only if operation. 73 00:06:12,200 --> 00:06:17,528 Let's get started. R is here, So what is not R every 74 00:06:17,528 --> 00:06:21,080 true becomes false an every force becomes true. 75 00:06:25,040 --> 00:06:29,967 So now which are the two columns that I need to combine together 76 00:06:29,967 --> 00:06:32,999 to find Q and not RI need Q? 77 00:06:34,670 --> 00:06:36,210 And I need not R. 78 00:06:37,470 --> 00:06:42,462 So and operation the end only returns true if both of the 79 00:06:42,462 --> 00:06:47,870 inputs are true. So I'm going to try to filter those ones out. 80 00:06:53,540 --> 00:06:58,314 And the rest of them I'm going to fill in with force. Now, if 81 00:06:58,314 --> 00:07:02,747 you are not using lined paper, then you want to be very careful 82 00:07:02,747 --> 00:07:06,157 about making sure that you lining these trees and force 83 00:07:06,157 --> 00:07:09,908 values relatively easy to see, because if you are getting a 84 00:07:09,908 --> 00:07:14,341 little bit wonky then you might take a force for the upper or 85 00:07:14,341 --> 00:07:18,433 lower row instead of the road that it belongs to. So be 86 00:07:18,433 --> 00:07:21,843 careful with that. Now I've got Q and not R. 87 00:07:22,100 --> 00:07:27,235 But what I need here now is the if and only if table. 88 00:07:28,090 --> 00:07:32,602 Remember if and only if it's true. If the two input values 89 00:07:32,602 --> 00:07:37,114 are exactly the same and it's false if the input values are 90 00:07:37,114 --> 00:07:41,626 different. So which columns am I going to use here? But I 91 00:07:41,626 --> 00:07:43,130 need to use P. 92 00:07:45,310 --> 00:07:50,910 And I need to use the Q and not R, which we just calculated 93 00:07:50,910 --> 00:07:56,110 here. So if they are the same, I'm going to return true. If 94 00:07:56,110 --> 00:08:00,510 they are the different, I'm going to return force. So look 95 00:08:00,510 --> 00:08:04,910 at this through force different. So I'm returning a force true 96 00:08:04,910 --> 00:08:08,910 through the same. I'm returning a true true enforce different. 97 00:08:08,910 --> 00:08:12,510 I'm returning a horse through unforced, different returning or 98 00:08:12,510 --> 00:08:14,910 force force and force the same. 99 00:08:15,050 --> 00:08:19,790 I'm returning a tree 4th century different. I'm returning a 100 00:08:19,790 --> 00:08:24,420 force. Force and force the same. I'm returning a true and 101 00:08:24,420 --> 00:08:27,750 force on force the same. Again, I'm returning the true. 102 00:08:29,690 --> 00:08:33,110 I hope you are gaining confidence in finding solutions 103 00:08:33,110 --> 00:08:38,430 to trig tables now in the next couple of videos we will look at 104 00:08:38,430 --> 00:08:42,230 some more difficult examples. However, now it's your turn to 105 00:08:42,230 --> 00:08:46,030 do some practice questions. The answers are at the end. 106 00:08:46,850 --> 00:08:48,830 So these are the practice questions. 107 00:08:54,940 --> 00:08:56,480 And here are the answers.