[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:18.18,0:00:22.42,Default,,0000,0000,0000,,Welcome to the next video. In\Nthe Boolean series. In this
Dialogue: 0,0:00:22.42,0:00:26.26,Default,,0000,0000,0000,,video we will look at some\Nmore examples of relatively
Dialogue: 0,0:00:26.26,0:00:27.42,Default,,0000,0000,0000,,simple trick tables.
Dialogue: 0,0:00:28.84,0:00:33.14,Default,,0000,0000,0000,,Now let's look at an\Nexample, which is a slightly
Dialogue: 0,0:00:33.14,0:00:34.86,Default,,0000,0000,0000,,bit more difficult, not.
Dialogue: 0,0:00:36.59,0:00:38.03,Default,,0000,0000,0000,,P or Q.
Dialogue: 0,0:00:39.32,0:00:45.25,Default,,0000,0000,0000,,And are so in this case now I\Nhave got three different inputs
Dialogue: 0,0:00:45.25,0:00:49.81,Default,,0000,0000,0000,,because I have got three\Ndifferent letters, so the number
Dialogue: 0,0:00:49.81,0:00:55.28,Default,,0000,0000,0000,,of rows in my throught table\Nwhich is calculated by two to
Dialogue: 0,0:00:55.28,0:01:01.72,Default,,0000,0000,0000,,the N. In this case an the\Nnumber of inputs is 3, therefore
Dialogue: 0,0:01:01.72,0:01:07.84,Default,,0000,0000,0000,,this will be two to three, which\Nis 8. So I have got P.
Dialogue: 0,0:01:08.87,0:01:15.46,Default,,0000,0000,0000,,I have got Q and I have caught\NR and the input combination half
Dialogue: 0,0:01:15.46,0:01:22.53,Default,,0000,0000,0000,,of eight is 4, so I'm going to\Ncopy four trues an I'm going to
Dialogue: 0,0:01:22.53,0:01:23.94,Default,,0000,0000,0000,,copy for forces.
Dialogue: 0,0:01:25.67,0:01:29.99,Default,,0000,0000,0000,,Then I'm just going to copy\Ntwo truths, two forces
Dialogue: 0,0:01:29.99,0:01:34.74,Default,,0000,0000,0000,,until I finish filling the\Ntable, and then in the last
Dialogue: 0,0:01:34.74,0:01:39.49,Default,,0000,0000,0000,,column I'm just going to do\Nthem, alternating 1 by 1.
Dialogue: 0,0:01:42.64,0:01:47.35,Default,,0000,0000,0000,,Now, in this case you can see\Nthat I have got every different
Dialogue: 0,0:01:47.35,0:01:50.97,Default,,0000,0000,0000,,combinations and I'm not\Nrepeating any one of them, so
Dialogue: 0,0:01:50.97,0:01:55.67,Default,,0000,0000,0000,,this is the starting of the\Nsetup of the table. Now what are
Dialogue: 0,0:01:55.67,0:01:59.29,Default,,0000,0000,0000,,the intermediate steps before we\Ncan actually find the final
Dialogue: 0,0:01:59.29,0:02:03.64,Default,,0000,0000,0000,,answer for the output? Now there\Nis a bracket and within the
Dialogue: 0,0:02:03.64,0:02:09.79,Default,,0000,0000,0000,,bracket I have got P or QP or Q\Nwill have to be one. I need to
Dialogue: 0,0:02:09.79,0:02:14.21,Default,,0000,0000,0000,,calculate. But then there is\Na node operation in front, so
Dialogue: 0,0:02:14.21,0:02:19.13,Default,,0000,0000,0000,,I going to have to apply that\Nto the output of P or Q and
Dialogue: 0,0:02:19.13,0:02:22.41,Default,,0000,0000,0000,,then at the end I'm going to\Nhave to use.
Dialogue: 0,0:02:24.85,0:02:30.81,Default,,0000,0000,0000,,The end operation to combine\Neverything together so P or Q,
Dialogue: 0,0:02:30.81,0:02:38.40,Default,,0000,0000,0000,,I'm going to use this table. Now\Nwhat do I know about the OR
Dialogue: 0,0:02:38.40,0:02:45.45,Default,,0000,0000,0000,,the OR only returns force if\Nboth of the inputs are force? So
Dialogue: 0,0:02:45.45,0:02:51.95,Default,,0000,0000,0000,,I'm going to run through the\Ntable and find the only inputs
Dialogue: 0,0:02:51.95,0:02:55.20,Default,,0000,0000,0000,,when both of them are force.
Dialogue: 0,0:02:55.53,0:02:59.49,Default,,0000,0000,0000,,And the rest of them I can just\Nquickly fill in.
Dialogue: 0,0:03:00.28,0:03:04.34,Default,,0000,0000,0000,,By truth, I could have gone\Nthrough two or two, gives me
Dialogue: 0,0:03:04.34,0:03:08.73,Default,,0000,0000,0000,,through three or two, gives me\Nthrough, etc. But this one is a
Dialogue: 0,0:03:08.73,0:03:10.42,Default,,0000,0000,0000,,nice and easy shortcut to
Dialogue: 0,0:03:10.42,0:03:12.97,Default,,0000,0000,0000,,remember. What does the note do?
Dialogue: 0,0:03:13.98,0:03:18.80,Default,,0000,0000,0000,,Change three to force and change\Nforced to true so the top half
Dialogue: 0,0:03:18.80,0:03:23.63,Default,,0000,0000,0000,,up to here is true. So every one\Nof them will be force.
Dialogue: 0,0:03:27.10,0:03:32.21,Default,,0000,0000,0000,,And the bottom two forces which\Nget then will turn into truth.
Dialogue: 0,0:03:32.21,0:03:38.60,Default,,0000,0000,0000,,And then I have to do the final\Ncombination of not P or Q&R. So
Dialogue: 0,0:03:38.60,0:03:44.57,Default,,0000,0000,0000,,which are the two that I need to\Ncombine together? Here I need to
Dialogue: 0,0:03:44.57,0:03:45.84,Default,,0000,0000,0000,,use this input.
Dialogue: 0,0:03:47.36,0:03:49.49,Default,,0000,0000,0000,,And I need to use the R.
Dialogue: 0,0:03:50.83,0:03:56.93,Default,,0000,0000,0000,,And what do I know about the end\Nand is only true if both of them
Dialogue: 0,0:03:56.93,0:04:01.50,Default,,0000,0000,0000,,are true? So I'm going to go\Nthrough the Roseanne. I'm going
Dialogue: 0,0:04:01.50,0:04:06.83,Default,,0000,0000,0000,,to filter out. Do I have double\Ntrues in here? I have one in
Dialogue: 0,0:04:06.83,0:04:12.31,Default,,0000,0000,0000,,here. And I haven't got it\Nanywhere else, so the rest of
Dialogue: 0,0:04:12.31,0:04:16.32,Default,,0000,0000,0000,,them will have to be filled in\Nwith forces becausw.
Dialogue: 0,0:04:17.12,0:04:22.45,Default,,0000,0000,0000,,And it's only true if both of\Nthe inputs are true. In any
Dialogue: 0,0:04:22.45,0:04:26.96,Default,,0000,0000,0000,,other cases, the end will be\Nforce, so knowing this shortcuts
Dialogue: 0,0:04:26.96,0:04:31.47,Default,,0000,0000,0000,,can save you quite some time on\Nfilling in the tables.
Dialogue: 0,0:04:32.88,0:04:37.15,Default,,0000,0000,0000,,And now let's look at the last\Nexample for this video.
Dialogue: 0,0:04:38.61,0:04:41.88,Default,,0000,0000,0000,,P. If only if.
Dialogue: 0,0:04:43.03,0:04:49.79,Default,,0000,0000,0000,,Q and not R. So this is\Na similar example to the
Dialogue: 0,0:04:49.79,0:04:55.42,Default,,0000,0000,0000,,previous one because PQ&R I've\Nagain have got three different
Dialogue: 0,0:04:55.42,0:04:57.10,Default,,0000,0000,0000,,inputs, so P.
Dialogue: 0,0:04:59.26,0:04:59.93,Default,,0000,0000,0000,,Q.
Dialogue: 0,0:05:01.65,0:05:02.10,Default,,0000,0000,0000,,R.
Dialogue: 0,0:05:06.05,0:05:11.06,Default,,0000,0000,0000,,Due to the power three gives\Nme 8, so it's to start the
Dialogue: 0,0:05:11.06,0:05:14.90,Default,,0000,0000,0000,,through table of correctly.\NI'm going to have to place
Dialogue: 0,0:05:14.90,0:05:16.83,Default,,0000,0000,0000,,than four truth four forces.
Dialogue: 0,0:05:19.00,0:05:22.22,Default,,0000,0000,0000,,Two truth 246.
Dialogue: 0,0:05:24.89,0:05:27.63,Default,,0000,0000,0000,,And then just alternating\Nthem 1 by 1.
Dialogue: 0,0:05:31.83,0:05:35.52,Default,,0000,0000,0000,,Right set up starting, setup,\Ndone correctly. Then what do I
Dialogue: 0,0:05:35.52,0:05:39.20,Default,,0000,0000,0000,,need to look at? I need to look\Nat my priorities.
Dialogue: 0,0:05:40.03,0:05:44.38,Default,,0000,0000,0000,,There is a bracket here and\Ninside the bracket that is Q and
Dialogue: 0,0:05:44.38,0:05:49.08,Default,,0000,0000,0000,,not R to be able to combine\Ntogether Q and not our first I
Dialogue: 0,0:05:49.08,0:05:54.10,Default,,0000,0000,0000,,need to know what the values are\Nfor not R so that's what I need
Dialogue: 0,0:05:54.10,0:05:58.12,Default,,0000,0000,0000,,to calculate first. Once I've\Ngot the values for not RI can
Dialogue: 0,0:05:58.12,0:05:59.80,Default,,0000,0000,0000,,calculate Q and not R.
Dialogue: 0,0:06:01.70,0:06:06.86,Default,,0000,0000,0000,,And once that's done, I can\Ncombine P together with the Q
Dialogue: 0,0:06:06.86,0:06:11.16,Default,,0000,0000,0000,,and not R using the if and\Nonly if operation.
Dialogue: 0,0:06:12.20,0:06:17.53,Default,,0000,0000,0000,,Let's get started. R is\Nhere, So what is not R every
Dialogue: 0,0:06:17.53,0:06:21.08,Default,,0000,0000,0000,,true becomes false an every\Nforce becomes true.
Dialogue: 0,0:06:25.04,0:06:29.97,Default,,0000,0000,0000,,So now which are the two columns\Nthat I need to combine together
Dialogue: 0,0:06:29.97,0:06:32.100,Default,,0000,0000,0000,,to find Q and not RI need Q?
Dialogue: 0,0:06:34.67,0:06:36.21,Default,,0000,0000,0000,,And I need not R.
Dialogue: 0,0:06:37.47,0:06:42.46,Default,,0000,0000,0000,,So and operation the end only\Nreturns true if both of the
Dialogue: 0,0:06:42.46,0:06:47.87,Default,,0000,0000,0000,,inputs are true. So I'm going to\Ntry to filter those ones out.
Dialogue: 0,0:06:53.54,0:06:58.31,Default,,0000,0000,0000,,And the rest of them I'm going\Nto fill in with force. Now, if
Dialogue: 0,0:06:58.31,0:07:02.75,Default,,0000,0000,0000,,you are not using lined paper,\Nthen you want to be very careful
Dialogue: 0,0:07:02.75,0:07:06.16,Default,,0000,0000,0000,,about making sure that you\Nlining these trees and force
Dialogue: 0,0:07:06.16,0:07:09.91,Default,,0000,0000,0000,,values relatively easy to see,\Nbecause if you are getting a
Dialogue: 0,0:07:09.91,0:07:14.34,Default,,0000,0000,0000,,little bit wonky then you might\Ntake a force for the upper or
Dialogue: 0,0:07:14.34,0:07:18.43,Default,,0000,0000,0000,,lower row instead of the road\Nthat it belongs to. So be
Dialogue: 0,0:07:18.43,0:07:21.84,Default,,0000,0000,0000,,careful with that. Now I've got\NQ and not R.
Dialogue: 0,0:07:22.10,0:07:27.24,Default,,0000,0000,0000,,But what I need here now is the\Nif and only if table.
Dialogue: 0,0:07:28.09,0:07:32.60,Default,,0000,0000,0000,,Remember if and only if it's\Ntrue. If the two input values
Dialogue: 0,0:07:32.60,0:07:37.11,Default,,0000,0000,0000,,are exactly the same and it's\Nfalse if the input values are
Dialogue: 0,0:07:37.11,0:07:41.63,Default,,0000,0000,0000,,different. So which columns am\NI going to use here? But I
Dialogue: 0,0:07:41.63,0:07:43.13,Default,,0000,0000,0000,,need to use P.
Dialogue: 0,0:07:45.31,0:07:50.91,Default,,0000,0000,0000,,And I need to use the Q and not\NR, which we just calculated
Dialogue: 0,0:07:50.91,0:07:56.11,Default,,0000,0000,0000,,here. So if they are the same,\NI'm going to return true. If
Dialogue: 0,0:07:56.11,0:08:00.51,Default,,0000,0000,0000,,they are the different, I'm\Ngoing to return force. So look
Dialogue: 0,0:08:00.51,0:08:04.91,Default,,0000,0000,0000,,at this through force different.\NSo I'm returning a force true
Dialogue: 0,0:08:04.91,0:08:08.91,Default,,0000,0000,0000,,through the same. I'm returning\Na true true enforce different.
Dialogue: 0,0:08:08.91,0:08:12.51,Default,,0000,0000,0000,,I'm returning a horse through\Nunforced, different returning or
Dialogue: 0,0:08:12.51,0:08:14.91,Default,,0000,0000,0000,,force force and force the same.
Dialogue: 0,0:08:15.05,0:08:19.79,Default,,0000,0000,0000,,I'm returning a tree 4th century\Ndifferent. I'm returning a
Dialogue: 0,0:08:19.79,0:08:24.42,Default,,0000,0000,0000,,force. Force and force the\Nsame. I'm returning a true and
Dialogue: 0,0:08:24.42,0:08:27.75,Default,,0000,0000,0000,,force on force the same.\NAgain, I'm returning the true.
Dialogue: 0,0:08:29.69,0:08:33.11,Default,,0000,0000,0000,,I hope you are gaining\Nconfidence in finding solutions
Dialogue: 0,0:08:33.11,0:08:38.43,Default,,0000,0000,0000,,to trig tables now in the next\Ncouple of videos we will look at
Dialogue: 0,0:08:38.43,0:08:42.23,Default,,0000,0000,0000,,some more difficult examples.\NHowever, now it's your turn to
Dialogue: 0,0:08:42.23,0:08:46.03,Default,,0000,0000,0000,,do some practice questions. The\Nanswers are at the end.
Dialogue: 0,0:08:46.85,0:08:48.83,Default,,0000,0000,0000,,So these are the practice\Nquestions.
Dialogue: 0,0:08:54.94,0:08:56.48,Default,,0000,0000,0000,,And here are the answers.