[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:19.18,0:00:23.16,Default,,0000,0000,0000,,Welcome to the second video on\NBoolean logic and in this video
Dialogue: 0,0:00:23.16,0:00:27.81,Default,,0000,0000,0000,,I would like to expose you to\Nthe laws of logic. Now we know
Dialogue: 0,0:00:27.81,0:00:30.80,Default,,0000,0000,0000,,now the different operations,\Nbut like with everything else
Dialogue: 0,0:00:30.80,0:00:34.78,Default,,0000,0000,0000,,in mathematics, there has to be\Nsome sort of rule that governs
Dialogue: 0,0:00:34.78,0:00:38.10,Default,,0000,0000,0000,,these operations. So let's go\Nthrough these loads of logics.
Dialogue: 0,0:00:38.10,0:00:42.09,Default,,0000,0000,0000,,The first load that I would\Nlike to mention to you. It's
Dialogue: 0,0:00:42.09,0:00:43.42,Default,,0000,0000,0000,,called this double negative.
Dialogue: 0,0:00:48.60,0:00:51.64,Default,,0000,0000,0000,,Basically, what happens\Nif I apply?
Dialogue: 0,0:00:52.73,0:00:55.02,Default,,0000,0000,0000,,The negation or the not?
Dialogue: 0,0:00:55.88,0:00:57.77,Default,,0000,0000,0000,,Twice to the same input.
Dialogue: 0,0:00:58.90,0:01:03.54,Default,,0000,0000,0000,,But think about it,\Nwhat is not not P?
Dialogue: 0,0:01:05.31,0:01:12.34,Default,,0000,0000,0000,,But if P is true then not P\Nis force and not force is true.
Dialogue: 0,0:01:12.34,0:01:18.44,Default,,0000,0000,0000,,So I end up with the origonal\Nvalue that I started with and
Dialogue: 0,0:01:18.44,0:01:20.32,Default,,0000,0000,0000,,remember that these three.
Dialogue: 0,0:01:21.29,0:01:24.63,Default,,0000,0000,0000,,Lines together it's not just\Nsimply equal, is logically
Dialogue: 0,0:01:24.63,0:01:29.82,Default,,0000,0000,0000,,equivalent, so it doesn't matter\Nif I write not not P or Pi. Am
Dialogue: 0,0:01:29.82,0:01:33.90,Default,,0000,0000,0000,,talking about exactly the same\Nthing, so they are very, very
Dialogue: 0,0:01:33.90,0:01:37.98,Default,,0000,0000,0000,,closely connected. That was the\Nfirst low. Let's look at the
Dialogue: 0,0:01:37.98,0:01:42.07,Default,,0000,0000,0000,,next loop, which we call the\Nimportant low. Now this is
Dialogue: 0,0:01:42.07,0:01:46.15,Default,,0000,0000,0000,,important. Low gives us some\Ninformation about what to do. If
Dialogue: 0,0:01:46.15,0:01:50.60,Default,,0000,0000,0000,,I applied the operation the same\Ninput. So P&P. What is that
Dialogue: 0,0:01:50.60,0:01:52.08,Default,,0000,0000,0000,,going to give me?
Dialogue: 0,0:01:52.89,0:01:58.47,Default,,0000,0000,0000,,Well, P&P always going to\Ngive me PY.
Dialogue: 0,0:02:00.13,0:02:06.01,Default,,0000,0000,0000,,If P is true, then true and true\Ngives me true, which is what P
Dialogue: 0,0:02:06.01,0:02:11.11,Default,,0000,0000,0000,,was. And if P is force than\Nforce and force gives me force
Dialogue: 0,0:02:11.11,0:02:16.59,Default,,0000,0000,0000,,which is again what P was. How\Ndoes that change if I have got
Dialogue: 0,0:02:16.59,0:02:17.77,Default,,0000,0000,0000,,the OR operation?
Dialogue: 0,0:02:18.37,0:02:23.97,Default,,0000,0000,0000,,P or P, but doesn't really\Nchange because I end up again
Dialogue: 0,0:02:23.97,0:02:28.64,Default,,0000,0000,0000,,with the same thing. True or\Ntrue gives me true.
Dialogue: 0,0:02:29.24,0:02:33.30,Default,,0000,0000,0000,,Which was P1 force or\Nforce again gives me
Dialogue: 0,0:02:33.30,0:02:35.10,Default,,0000,0000,0000,,force which was P.
Dialogue: 0,0:02:37.63,0:02:41.65,Default,,0000,0000,0000,,Let's look at the identity low\Nand this low. Now talking about
Dialogue: 0,0:02:41.65,0:02:45.34,Default,,0000,0000,0000,,what happens if I combine\Ntogether and input with a true
Dialogue: 0,0:02:45.34,0:02:46.34,Default,,0000,0000,0000,,or false value.
Dialogue: 0,0:02:47.22,0:02:50.04,Default,,0000,0000,0000,,Soupy and true.
Dialogue: 0,0:02:51.59,0:02:55.24,Default,,0000,0000,0000,,What is that logically\Nequivalent to think about it?
Dialogue: 0,0:02:56.63,0:03:01.75,Default,,0000,0000,0000,,If three is true, true and true\Nwill give me true, which was the
Dialogue: 0,0:03:01.75,0:03:07.24,Default,,0000,0000,0000,,same as P. But if P is force\Nforce and two gives me force, so
Dialogue: 0,0:03:07.24,0:03:12.73,Default,,0000,0000,0000,,it doesn't matter if P is 2 or\N4. If I combined together P with
Dialogue: 0,0:03:12.73,0:03:17.49,Default,,0000,0000,0000,,an with a true using the end\Noperation, I always going to end
Dialogue: 0,0:03:17.49,0:03:21.52,Default,,0000,0000,0000,,up with what P was. This true\Ndoesn't really make any
Dialogue: 0,0:03:21.52,0:03:23.35,Default,,0000,0000,0000,,difference in that what happens
Dialogue: 0,0:03:23.35,0:03:29.70,Default,,0000,0000,0000,,now? If I use P or the\Nforce symbol in here, Now if P
Dialogue: 0,0:03:29.70,0:03:35.12,Default,,0000,0000,0000,,was true, two or four's give me\Nthe true. But if P was forced
Dialogue: 0,0:03:35.12,0:03:40.15,Default,,0000,0000,0000,,force or force again gives me\Nthe force. So again I'm going to
Dialogue: 0,0:03:40.15,0:03:45.18,Default,,0000,0000,0000,,end up with what P was soapy or\Nforce is logically equivalent to
Dialogue: 0,0:03:45.18,0:03:49.44,Default,,0000,0000,0000,,pee. Now these loads of logic\Nare really helpful because if
Dialogue: 0,0:03:49.44,0:03:54.08,Default,,0000,0000,0000,,you have got a long complicated\Nlogic sentence and you want to
Dialogue: 0,0:03:54.08,0:03:55.24,Default,,0000,0000,0000,,make it simpler.
Dialogue: 0,0:03:55.34,0:03:59.07,Default,,0000,0000,0000,,These are the rules. These are\Nthe laws that you can apply to
Dialogue: 0,0:03:59.07,0:04:02.52,Default,,0000,0000,0000,,break that complication down and\Nsee a little bit easier what is
Dialogue: 0,0:04:02.52,0:04:06.33,Default,,0000,0000,0000,,actually going on. The next load\Nis the only elation.
Dialogue: 0,0:04:07.63,0:04:12.99,Default,,0000,0000,0000,,And the only elation is kind of\Ntelling you when would your
Dialogue: 0,0:04:12.99,0:04:17.91,Default,,0000,0000,0000,,input on Hill eight disappear.\NSo if you had called P.
Dialogue: 0,0:04:18.67,0:04:21.87,Default,,0000,0000,0000,,And force. Remember.
Dialogue: 0,0:04:23.23,0:04:27.14,Default,,0000,0000,0000,,Once you have got force in the\Nend gate, which was two types on
Dialogue: 0,0:04:27.14,0:04:31.02,Default,,0000,0000,0000,,the same pipe. It doesn't matter\Nif P is on or off.
Dialogue: 0,0:04:31.77,0:04:36.01,Default,,0000,0000,0000,,Water won't go through, so this\Nis always going to be force.
Dialogue: 0,0:04:36.94,0:04:41.48,Default,,0000,0000,0000,,And what happens if you have got\NP or true?
Dialogue: 0,0:04:42.80,0:04:46.73,Default,,0000,0000,0000,,Basically, this is when you add\Ntwo branches of the water and it
Dialogue: 0,0:04:46.73,0:04:50.35,Default,,0000,0000,0000,,doesn't matter if piece turned\Non or off the water will always
Dialogue: 0,0:04:50.35,0:04:53.97,Default,,0000,0000,0000,,be able to flow through the\Nother branch, so this is always
Dialogue: 0,0:04:53.97,0:04:55.18,Default,,0000,0000,0000,,going to be true.
Dialogue: 0,0:04:57.24,0:04:59.33,Default,,0000,0000,0000,,The next low is the inverse low.
Dialogue: 0,0:05:02.52,0:05:07.08,Default,,0000,0000,0000,,So what happens if I add\Ntogether P and not P?
Dialogue: 0,0:05:08.36,0:05:13.56,Default,,0000,0000,0000,,Well, if P is true then not\NP is force.
Dialogue: 0,0:05:14.17,0:05:19.72,Default,,0000,0000,0000,,And two through an force gives\Nme force. But what happens if P
Dialogue: 0,0:05:19.72,0:05:22.28,Default,,0000,0000,0000,,is force if P is force?
Dialogue: 0,0:05:23.06,0:05:26.04,Default,,0000,0000,0000,,Then not P is true, but.
Dialogue: 0,0:05:26.61,0:05:31.36,Default,,0000,0000,0000,,False and true are still force.\NSo in this case I'm always going
Dialogue: 0,0:05:31.36,0:05:33.91,Default,,0000,0000,0000,,to end up with a force answer.
Dialogue: 0,0:05:34.84,0:05:38.94,Default,,0000,0000,0000,,And what happens if I have got P\Nor not P?
Dialogue: 0,0:05:40.49,0:05:45.15,Default,,0000,0000,0000,,If P is true, not B is force,\Nbut remember one of them is
Dialogue: 0,0:05:45.15,0:05:49.48,Default,,0000,0000,0000,,true, so I'm going to end up\Nwith a true sign in here.
Dialogue: 0,0:05:51.25,0:05:55.53,Default,,0000,0000,0000,,If P is false, then not paying\Nhistory. So again I have got a
Dialogue: 0,0:05:55.53,0:05:59.51,Default,,0000,0000,0000,,true sign in here, so I will\Nbe able to get through with
Dialogue: 0,0:05:59.51,0:06:02.57,Default,,0000,0000,0000,,the water, so this is always\Ngoing to be true.
Dialogue: 0,0:06:05.46,0:06:08.74,Default,,0000,0000,0000,,Next, look commutative. You\Nprobably familiar with this
Dialogue: 0,0:06:08.74,0:06:12.84,Default,,0000,0000,0000,,term. You might have heard it\Naddition and sub multiplications
Dialogue: 0,0:06:12.84,0:06:16.94,Default,,0000,0000,0000,,are being commutative and in\Nthere. Basically what you meant
Dialogue: 0,0:06:16.94,0:06:24.32,Default,,0000,0000,0000,,by is that 2 + 3 is same as\N3 + 2 or 2 * 3 is the
Dialogue: 0,0:06:24.32,0:06:29.24,Default,,0000,0000,0000,,same as 3 * 2, and that's\Nexactly what we mean by
Dialogue: 0,0:06:29.24,0:06:34.98,Default,,0000,0000,0000,,commutative in here. P&Q is the\Nsame as Q&P and I can also say
Dialogue: 0,0:06:34.98,0:06:41.50,Default,,0000,0000,0000,,that. P or Q is exactly the same\Nas Q or P, so the operation in
Dialogue: 0,0:06:41.50,0:06:45.91,Default,,0000,0000,0000,,which I put these inputs in\Ndoesn't make difference as far
Dialogue: 0,0:06:45.91,0:06:49.92,Default,,0000,0000,0000,,as the output concerned. Another\Nload that you probably familiar
Dialogue: 0,0:06:49.92,0:06:53.93,Default,,0000,0000,0000,,with from algebra is associative\Nlife. Remember that you could
Dialogue: 0,0:06:53.93,0:06:58.74,Default,,0000,0000,0000,,use the brackets and you can\Ncombine the brackets as long as
Dialogue: 0,0:06:58.74,0:07:03.15,Default,,0000,0000,0000,,the same operation is concerned.\NSo what I mean by B&Q?
Dialogue: 0,0:07:04.30,0:07:12.00,Default,,0000,0000,0000,,And R is exactly the same as\NP&Q&R. Or if I apply to the
Dialogue: 0,0:07:12.00,0:07:14.55,Default,,0000,0000,0000,,operation. P or Q.
Dialogue: 0,0:07:15.56,0:07:22.09,Default,,0000,0000,0000,,Or are is exactly the same as P\Nor key or R? So as far as I'm
Dialogue: 0,0:07:22.09,0:07:25.16,Default,,0000,0000,0000,,using exactly the same\Noperations, doesn't matter where
Dialogue: 0,0:07:25.16,0:07:29.77,Default,,0000,0000,0000,,I place the bracket, the bracket\Ncan be flexibly placed an it's
Dialogue: 0,0:07:29.77,0:07:34.38,Default,,0000,0000,0000,,again sometimes quite good to\Nknow to move around and be able
Dialogue: 0,0:07:34.38,0:07:37.06,Default,,0000,0000,0000,,to manipulate these expressions\Nto simplify them.
Dialogue: 0,0:07:38.90,0:07:43.09,Default,,0000,0000,0000,,One more low that could\Nbe familiar from algebra
Dialogue: 0,0:07:43.09,0:07:44.96,Default,,0000,0000,0000,,is the distributive law.
Dialogue: 0,0:07:46.38,0:07:52.88,Default,,0000,0000,0000,,And what the distributive law\Ntells you that is P&Q or R
Dialogue: 0,0:07:52.88,0:07:55.05,Default,,0000,0000,0000,,can be written as.
Dialogue: 0,0:07:56.66,0:07:57.86,Default,,0000,0000,0000,,B&Q
Dialogue: 0,0:07:59.00,0:08:03.85,Default,,0000,0000,0000,,or P&R. So what's\Ngoing on in here?
Dialogue: 0,0:08:06.12,0:08:12.20,Default,,0000,0000,0000,,Your end operator distributed\Namongst the two other inputs
Dialogue: 0,0:08:12.20,0:08:15.57,Default,,0000,0000,0000,,and your or operator now.
Dialogue: 0,0:08:16.44,0:08:19.05,Default,,0000,0000,0000,,Become in between the brackets.
Dialogue: 0,0:08:20.49,0:08:24.28,Default,,0000,0000,0000,,And what happens\Nif I change these?
Dialogue: 0,0:08:25.53,0:08:28.15,Default,,0000,0000,0000,,Operators if I use the OR here.
Dialogue: 0,0:08:29.01,0:08:30.09,Default,,0000,0000,0000,,And the end here.
Dialogue: 0,0:08:31.95,0:08:33.18,Default,,0000,0000,0000,,This is the same again.
Dialogue: 0,0:08:35.00,0:08:37.13,Default,,0000,0000,0000,,P. Or Q.
Dialogue: 0,0:08:38.19,0:08:44.95,Default,,0000,0000,0000,,And P or R. So again, I\Ncan distribute my or operator.
Dialogue: 0,0:08:46.90,0:08:51.01,Default,,0000,0000,0000,,Into the brackets and I can keep\Nthe end operator between.
Dialogue: 0,0:08:51.67,0:08:57.72,Default,,0000,0000,0000,,The brackets this is similar to\Nwhat happens in mathematics. If
Dialogue: 0,0:08:57.72,0:09:05.42,Default,,0000,0000,0000,,you remember 2 * 3 + X,\Nyou can rewrite it as 2 *
Dialogue: 0,0:09:05.42,0:09:11.81,Default,,0000,0000,0000,,3 plus. Two times the X. OK,\Nso you're plus now here become.
Dialogue: 0,0:09:12.41,0:09:15.40,Default,,0000,0000,0000,,The one in the middle and\Nthe multiplication
Dialogue: 0,0:09:15.40,0:09:16.90,Default,,0000,0000,0000,,distributed over the\Naddition.
Dialogue: 0,0:09:19.41,0:09:23.39,Default,,0000,0000,0000,,Now I have introduced you to\Nquite a few laws of logic. In a
Dialogue: 0,0:09:23.39,0:09:26.51,Default,,0000,0000,0000,,further video I will show you\Nthe rest of the lows.