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Welcome to the second video on[br]Boolean logic and in this video

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

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now the different operations,[br]but like with everything else

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

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

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

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called this double negative.

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Basically, what happens[br]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,[br]what is not not P?

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But if P is true then not P[br]is force and not force is true.

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So I end up with the origonal[br]value that I started with and

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remember that these three.

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

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

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talking about exactly the same[br]thing, so they are very, very

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

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

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

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I applied the operation the same[br]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[br]give me PY.

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If P is true, then true and true[br]gives me true, which is what P

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was. And if P is force than[br]force and force gives me force

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which is again what P was. How[br]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[br]change because I end up again

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with the same thing. True or[br]true gives me true.

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Which was P1 force or[br]force again gives me

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force which was P.

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

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what happens if I combine[br]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[br]equivalent to think about it?

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

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

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

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

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up with what P was. This true[br]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[br]force symbol in here, Now if P

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

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

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

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

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you have got a long complicated[br]logic sentence and you want to

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make it simpler.

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These are the rules. These are[br]the laws that you can apply to

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

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actually going on. The next load[br]is the only elation.

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

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

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And force. Remember.

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

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

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

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And what happens if you have got[br]P or true?

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

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

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be able to flow through the[br]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[br]together P and not P?

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Well, if P is true then not[br]P is force.

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And two through an force gives[br]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.[br]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[br]or not P?

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

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

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

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

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

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Next, look commutative. You[br]probably familiar with this

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term. You might have heard it[br]addition and sub multiplications

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are being commutative and in[br]there. Basically what you meant

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by is that 2 + 3 is same as[br]3 + 2 or 2 * 3 is the

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

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

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

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

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as the output concerned. Another[br]load that you probably familiar

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with from algebra is associative[br]life. Remember that you could

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use the brackets and you can[br]combine the brackets as long as

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

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And R is exactly the same as[br]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[br]or key or R? So as far as I'm

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using exactly the same[br]operations, doesn't matter where

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

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again sometimes quite good to[br]know to move around and be able

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to manipulate these expressions[br]to simplify them.

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One more low that could[br]be familiar from algebra

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is the distributive law.

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And what the distributive law[br]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[br]going on in here?

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Your end operator distributed[br]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[br]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[br]can distribute my or operator.

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Into the brackets and I can keep[br]the end operator between.

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

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

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

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The one in the middle and[br]the multiplication

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distributed over the[br]addition.

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

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further video I will show you[br]the rest of the lows.