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

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

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now the different operations,
but like with everything else

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

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

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

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called this double negative.

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Basically, what happens
if I apply?

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The negation or the not?

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Twice to the same input.

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But think about it,
what is not not P?

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

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

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remember that these three.

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

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

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

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

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

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

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

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going to give me?

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

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

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

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

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the OR operation?

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

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

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Which was P1 force or
force again gives me

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force which was P.

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

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what happens if I combine
together and input with a true

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or false value.

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Soupy and true.

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What is that logically
equivalent to think about it?

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

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

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

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

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

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difference in that what happens

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

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

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

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

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

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

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make it simpler.

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

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

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

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

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

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And force. Remember.

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

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

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

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And what happens if you have got
P or true?

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

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

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

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going to be true.

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The next low is the inverse low.

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

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

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

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is force if P is force?

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Then not P is true, but.

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

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to end up with a force answer.

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

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

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

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

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

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

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Next, look commutative. You
probably familiar with this

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term. You might have heard it
addition and sub multiplications

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are being commutative and in
there. Basically what you meant

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

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

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

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

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

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as the output concerned. Another
load that you probably familiar

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with from algebra is associative
life. Remember that you could

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

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

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

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operation. P or Q.

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

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using exactly the same
operations, doesn't matter where

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

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

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to manipulate these expressions
to simplify them.

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One more low that could
be familiar from algebra

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is the distributive law.

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

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can be written as.

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B&Q

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

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Your end operator distributed
amongst the two other inputs

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and your or operator now.

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Become in between the brackets.

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And what happens
if I change these?

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Operators if I use the OR here.

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And the end here.

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This is the same again.

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P. Or Q.

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

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

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

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

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

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The one in the middle and
the multiplication

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distributed over the
addition.

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

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