WEBVTT

00:00:19.180 --> 00:00:23.164
Welcome to the second video on
Boolean logic and in this video

00:00:23.164 --> 00:00:27.812
I would like to expose you to
the laws of logic. Now we know

00:00:27.812 --> 00:00:30.800
now the different operations,
but like with everything else

00:00:30.800 --> 00:00:34.784
in mathematics, there has to be
some sort of rule that governs

00:00:34.784 --> 00:00:38.104
these operations. So let's go
through these loads of logics.

00:00:38.104 --> 00:00:42.088
The first load that I would
like to mention to you. It's

00:00:42.088 --> 00:00:43.416
called this double negative.

00:00:48.600 --> 00:00:51.636
Basically, what happens
if I apply?

00:00:52.730 --> 00:00:55.020
The negation or the not?

00:00:55.880 --> 00:00:57.770
Twice to the same input.

00:00:58.900 --> 00:01:03.544
But think about it,
what is not not P?

00:01:05.310 --> 00:01:12.345
But if P is true then not P
is force and not force is true.

00:01:12.345 --> 00:01:18.442
So I end up with the origonal
value that I started with and

00:01:18.442 --> 00:01:20.318
remember that these three.

00:01:21.290 --> 00:01:24.629
Lines together it's not just
simply equal, is logically

00:01:24.629 --> 00:01:29.823
equivalent, so it doesn't matter
if I write not not P or Pi. Am

00:01:29.823 --> 00:01:33.904
talking about exactly the same
thing, so they are very, very

00:01:33.904 --> 00:01:37.985
closely connected. That was the
first low. Let's look at the

00:01:37.985 --> 00:01:42.066
next loop, which we call the
important low. Now this is

00:01:42.066 --> 00:01:46.147
important. Low gives us some
information about what to do. If

00:01:46.147 --> 00:01:50.599
I applied the operation the same
input. So P&P. What is that

00:01:50.599 --> 00:01:52.083
going to give me?

00:01:52.890 --> 00:01:58.466
Well, P&P always going to
give me PY.

00:02:00.130 --> 00:02:06.010
If P is true, then true and true
gives me true, which is what P

00:02:06.010 --> 00:02:11.106
was. And if P is force than
force and force gives me force

00:02:11.106 --> 00:02:16.594
which is again what P was. How
does that change if I have got

00:02:16.594 --> 00:02:17.770
the OR operation?

00:02:18.370 --> 00:02:23.974
P or P, but doesn't really
change because I end up again

00:02:23.974 --> 00:02:28.644
with the same thing. True or
true gives me true.

00:02:29.240 --> 00:02:33.299
Which was P1 force or
force again gives me

00:02:33.299 --> 00:02:35.103
force which was P.

00:02:37.630 --> 00:02:41.650
Let's look at the identity low
and this low. Now talking about

00:02:41.650 --> 00:02:45.335
what happens if I combine
together and input with a true

00:02:45.335 --> 00:02:46.340
or false value.

00:02:47.220 --> 00:02:50.040
Soupy and true.

00:02:51.590 --> 00:02:55.244
What is that logically
equivalent to think about it?

00:02:56.630 --> 00:03:01.754
If three is true, true and true
will give me true, which was the

00:03:01.754 --> 00:03:07.244
same as P. But if P is force
force and two gives me force, so

00:03:07.244 --> 00:03:12.734
it doesn't matter if P is 2 or
4. If I combined together P with

00:03:12.734 --> 00:03:17.492
an with a true using the end
operation, I always going to end

00:03:17.492 --> 00:03:21.518
up with what P was. This true
doesn't really make any

00:03:21.518 --> 00:03:23.348
difference in that what happens

00:03:23.348 --> 00:03:29.701
now? If I use P or the
force symbol in here, Now if P

00:03:29.701 --> 00:03:35.119
was true, two or four's give me
the true. But if P was forced

00:03:35.119 --> 00:03:40.150
force or force again gives me
the force. So again I'm going to

00:03:40.150 --> 00:03:45.181
end up with what P was soapy or
force is logically equivalent to

00:03:45.181 --> 00:03:49.438
pee. Now these loads of logic
are really helpful because if

00:03:49.438 --> 00:03:54.082
you have got a long complicated
logic sentence and you want to

00:03:54.082 --> 00:03:55.243
make it simpler.

00:03:55.340 --> 00:03:59.071
These are the rules. These are
the laws that you can apply to

00:03:59.071 --> 00:04:02.515
break that complication down and
see a little bit easier what is

00:04:02.515 --> 00:04:06.334
actually going on. The next load
is the only elation.

00:04:07.630 --> 00:04:12.994
And the only elation is kind of
telling you when would your

00:04:12.994 --> 00:04:17.911
input on Hill eight disappear.
So if you had called P.

00:04:18.670 --> 00:04:21.870
And force. Remember.

00:04:23.230 --> 00:04:27.136
Once you have got force in the
end gate, which was two types on

00:04:27.136 --> 00:04:31.015
the same pipe. It doesn't matter
if P is on or off.

00:04:31.770 --> 00:04:36.006
Water won't go through, so this
is always going to be force.

00:04:36.940 --> 00:04:41.480
And what happens if you have got
P or true?

00:04:42.800 --> 00:04:46.726
Basically, this is when you add
two branches of the water and it

00:04:46.726 --> 00:04:50.350
doesn't matter if piece turned
on or off the water will always

00:04:50.350 --> 00:04:53.974
be able to flow through the
other branch, so this is always

00:04:53.974 --> 00:04:55.182
going to be true.

00:04:57.240 --> 00:04:59.326
The next low is the inverse low.

00:05:02.520 --> 00:05:07.085
So what happens if I add
together P and not P?

00:05:08.360 --> 00:05:13.560
Well, if P is true then not
P is force.

00:05:14.170 --> 00:05:19.721
And two through an force gives
me force. But what happens if P

00:05:19.721 --> 00:05:22.283
is force if P is force?

00:05:23.060 --> 00:05:26.036
Then not P is true, but.

00:05:26.610 --> 00:05:31.355
False and true are still force.
So in this case I'm always going

00:05:31.355 --> 00:05:33.910
to end up with a force answer.

00:05:34.840 --> 00:05:38.943
And what happens if I have got P
or not P?

00:05:40.490 --> 00:05:45.152
If P is true, not B is force,
but remember one of them is

00:05:45.152 --> 00:05:49.481
true, so I'm going to end up
with a true sign in here.

00:05:51.250 --> 00:05:55.534
If P is false, then not paying
history. So again I have got a

00:05:55.534 --> 00:05:59.512
true sign in here, so I will
be able to get through with

00:05:59.512 --> 00:06:02.572
the water, so this is always
going to be true.

00:06:05.460 --> 00:06:08.740
Next, look commutative. You
probably familiar with this

00:06:08.740 --> 00:06:12.840
term. You might have heard it
addition and sub multiplications

00:06:12.840 --> 00:06:16.940
are being commutative and in
there. Basically what you meant

00:06:16.940 --> 00:06:24.320
by is that 2 + 3 is same as
3 + 2 or 2 * 3 is the

00:06:24.320 --> 00:06:29.240
same as 3 * 2, and that's
exactly what we mean by

00:06:29.240 --> 00:06:34.980
commutative in here. P&Q is the
same as Q&P and I can also say

00:06:34.980 --> 00:06:41.495
that. P or Q is exactly the same
as Q or P, so the operation in

00:06:41.495 --> 00:06:45.906
which I put these inputs in
doesn't make difference as far

00:06:45.906 --> 00:06:49.916
as the output concerned. Another
load that you probably familiar

00:06:49.916 --> 00:06:53.926
with from algebra is associative
life. Remember that you could

00:06:53.926 --> 00:06:58.738
use the brackets and you can
combine the brackets as long as

00:06:58.738 --> 00:07:03.149
the same operation is concerned.
So what I mean by B&Q?

00:07:04.300 --> 00:07:12.000
And R is exactly the same as
P&Q&R. Or if I apply to the

00:07:12.000 --> 00:07:14.550
operation. P or Q.

00:07:15.560 --> 00:07:22.088
Or are is exactly the same as P
or key or R? So as far as I'm

00:07:22.088 --> 00:07:25.160
using exactly the same
operations, doesn't matter where

00:07:25.160 --> 00:07:29.768
I place the bracket, the bracket
can be flexibly placed an it's

00:07:29.768 --> 00:07:34.376
again sometimes quite good to
know to move around and be able

00:07:34.376 --> 00:07:37.064
to manipulate these expressions
to simplify them.

00:07:38.900 --> 00:07:43.094
One more low that could
be familiar from algebra

00:07:43.094 --> 00:07:44.958
is the distributive law.

00:07:46.380 --> 00:07:52.884
And what the distributive law
tells you that is P&Q or R

00:07:52.884 --> 00:07:55.052
can be written as.

00:07:56.660 --> 00:07:57.860
B&Q

00:07:59.000 --> 00:08:03.848
or P&R. So what's
going on in here?

00:08:06.120 --> 00:08:12.195
Your end operator distributed
amongst the two other inputs

00:08:12.195 --> 00:08:15.570
and your or operator now.

00:08:16.440 --> 00:08:19.050
Become in between the brackets.

00:08:20.490 --> 00:08:24.277
And what happens
if I change these?

00:08:25.530 --> 00:08:28.148
Operators if I use the OR here.

00:08:29.010 --> 00:08:30.090
And the end here.

00:08:31.950 --> 00:08:33.180
This is the same again.

00:08:35.000 --> 00:08:37.130
P. Or Q.

00:08:38.190 --> 00:08:44.946
And P or R. So again, I
can distribute my or operator.

00:08:46.900 --> 00:08:51.014
Into the brackets and I can keep
the end operator between.

00:08:51.670 --> 00:08:57.720
The brackets this is similar to
what happens in mathematics. If

00:08:57.720 --> 00:09:05.420
you remember 2 * 3 + X,
you can rewrite it as 2 *

00:09:05.420 --> 00:09:11.810
3 plus. Two times the X. OK,
so you're plus now here become.

00:09:12.410 --> 00:09:15.402
The one in the middle and
the multiplication

00:09:15.402 --> 00:09:16.898
distributed over the
addition.

00:09:19.410 --> 00:09:23.386
Now I have introduced you to
quite a few laws of logic. In a

00:09:23.386 --> 00:09:26.510
further video I will show you
the rest of the lows.