Welcome to the second video on
Boolean logic and in this video

I would like to expose you to
the laws of logic. Now we know

now the different operations,
but like with everything else

in mathematics, there has to be
some sort of rule that governs

these operations. So let's go
through these loads of logics.

The first load that I would
like to mention to you. It's

called this double negative.

Basically, what happens
if I apply?

The negation or the not?

Twice to the same input.

But think about it,
what is not not P?

But if P is true then not P
is force and not force is true.

So I end up with the origonal
value that I started with and

remember that these three.

Lines together it's not just
simply equal, is logically

equivalent, so it doesn't matter
if I write not not P or Pi. Am

talking about exactly the same
thing, so they are very, very

closely connected. That was the
first low. Let's look at the

next loop, which we call the
important low. Now this is

important. Low gives us some
information about what to do. If

I applied the operation the same
input. So P&P. What is that

going to give me?

Well, P&P always going to
give me PY.

If P is true, then true and true
gives me true, which is what P

was. And if P is force than
force and force gives me force

which is again what P was. How
does that change if I have got

the OR operation?

P or P, but doesn't really
change because I end up again

with the same thing. True or
true gives me true.

Which was P1 force or
force again gives me

force which was P.

Let's look at the identity low
and this low. Now talking about

what happens if I combine
together and input with a true

or false value.

Soupy and true.

What is that logically
equivalent to think about it?

If three is true, true and true
will give me true, which was the

same as P. But if P is force
force and two gives me force, so

it doesn't matter if P is 2 or
4. If I combined together P with

an with a true using the end
operation, I always going to end

up with what P was. This true
doesn't really make any

difference in that what happens

now? If I use P or the
force symbol in here, Now if P

was true, two or four's give me
the true. But if P was forced

force or force again gives me
the force. So again I'm going to

end up with what P was soapy or
force is logically equivalent to

pee. Now these loads of logic
are really helpful because if

you have got a long complicated
logic sentence and you want to

make it simpler.

These are the rules. These are
the laws that you can apply to

break that complication down and
see a little bit easier what is

actually going on. The next load
is the only elation.

And the only elation is kind of
telling you when would your

input on Hill eight disappear.
So if you had called P.

And force. Remember.

Once you have got force in the
end gate, which was two types on

the same pipe. It doesn't matter
if P is on or off.

Water won't go through, so this
is always going to be force.

And what happens if you have got
P or true?

Basically, this is when you add
two branches of the water and it

doesn't matter if piece turned
on or off the water will always

be able to flow through the
other branch, so this is always

going to be true.

The next low is the inverse low.

So what happens if I add
together P and not P?

Well, if P is true then not
P is force.

And two through an force gives
me force. But what happens if P

is force if P is force?

Then not P is true, but.

False and true are still force.
So in this case I'm always going

to end up with a force answer.

And what happens if I have got P
or not P?

If P is true, not B is force,
but remember one of them is

true, so I'm going to end up
with a true sign in here.

If P is false, then not paying
history. So again I have got a

true sign in here, so I will
be able to get through with

the water, so this is always
going to be true.

Next, look commutative. You
probably familiar with this

term. You might have heard it
addition and sub multiplications

are being commutative and in
there. Basically what you meant

by is that 2 + 3 is same as
3 + 2 or 2 * 3 is the

same as 3 * 2, and that's
exactly what we mean by

commutative in here. P&Q is the
same as Q&P and I can also say

that. P or Q is exactly the same
as Q or P, so the operation in

which I put these inputs in
doesn't make difference as far

as the output concerned. Another
load that you probably familiar

with from algebra is associative
life. Remember that you could

use the brackets and you can
combine the brackets as long as

the same operation is concerned.
So what I mean by B&Q?

And R is exactly the same as
P&Q&R. Or if I apply to the

operation. P or Q.

Or are is exactly the same as P
or key or R? So as far as I'm

using exactly the same
operations, doesn't matter where

I place the bracket, the bracket
can be flexibly placed an it's

again sometimes quite good to
know to move around and be able

to manipulate these expressions
to simplify them.

One more low that could
be familiar from algebra

is the distributive law.

And what the distributive law
tells you that is P&Q or R

can be written as.

B&Q

or P&R. So what's
going on in here?

Your end operator distributed
amongst the two other inputs

and your or operator now.

Become in between the brackets.

And what happens
if I change these?

Operators if I use the OR here.

And the end here.

This is the same again.

P. Or Q.

And P or R. So again, I
can distribute my or operator.

Into the brackets and I can keep
the end operator between.

The brackets this is similar to
what happens in mathematics. If

you remember 2 * 3 + X,
you can rewrite it as 2 *

3 plus. Two times the X. OK,
so you're plus now here become.

The one in the middle and
the multiplication

distributed over the
addition.

Now I have introduced you to
quite a few laws of logic. In a

further video I will show you
the rest of the lows.