WEBVTT

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Welcome to the last video. In
the Boolean series. In this

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video we will look at some of
the more complicated Boolean

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expressions and therethrough
tables.

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Now let's make matters a
little bit more complicated.

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By using more brackets.

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P&R

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or
Q&R.

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If then. P or not Q first
thing that we want to establish

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is to find out how many
different inputs are there.

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BRQRPQ there are
altogether three different

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letters, so P.

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Q.

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R.

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Again, three different letters.
Two to three gives me 8, so I'm

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going to have eight different
input combinations or eight

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different rows in the truth
table. Half of it is 4, so I'm

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going to start with four truths
and then four forces.

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Then half of four is 2, so I'm
going to have two 2, two fours

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until I fill up the table.

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Then just use true force.

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The force to fill
in the last column.

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Now let's look at the different
brackets. I have got a square

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bracket here. Which is combining
together this bracket using the

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event operation. So to be able
to use the if then operation

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first I need to know what is the
value inside the square bracket,

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but unfortunately inside the
square bracket I have got two

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different brackets. So first I
need to calculate the P&R.

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Then I need to calculate
the Q&R.

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Then I will be able to calculate
what are the values in the

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square bracket, not to save some
space. I'm just going to put the

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square brackets sign into here.

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Now once I've got the square
bracket, I need to combine the

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values of the square bracket
with this bracket, but inside

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this bracket I have got an not Q
as well. So first I will need to

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calculate the value of not Q,
then I will be able to calculate

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the P or not Q values and once
I've got that I will be able to

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use the value for the event
operation. And because there are

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no other if their operations.

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I can use the even operation
here instead of having to write

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the whole thing out because then
that would again just take up

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too much space in here.

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So let's get started P&R I'm
using these two columns, the P

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and they are columns and I'm
using an end again. What do I

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know about the end and is only
true if both of them are true?

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This is true for both of them.
That is not so it will be

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forced. That's true for both of
them. That's going to give me

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true that is not gives me a
force that is not give me a

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force force force and force

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again. Then I'm going to have to
use the Q&R so Q&R both of them

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are true, gives me back a true
value. They are different. That

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gives me back of force value.

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They bought force that still
gives me a force value because

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it's the end. Both through gives
me true Force force force. Now

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that's great. What I need to do
next is to find out what is the

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overall value combinations in
the square bracket. Now in this

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work square bracket I'm
combining together these two

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using the OR. So this is this
column and that is this column

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and I'm going to need to combine
them together using the OR. What

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do I know about the?

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Or the OR is only force if both
of them are forced in every

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other case, is the OR returns
true? So that's true. This is

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force. That is true. That
is force true Force, force

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force. So I've got the
square bracket.

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Next thing I need is
the note QQ is here.

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So they're not. Q would be
just where Q is true, not

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QB LB force.

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An when Q is force not not Q
will be true.

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I've got the not key now and
what I need is the P or not Q.

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P or not, QP is this one.

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And not Q is this one that they
are quite far away from each

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other, but it just an or
operation. Again, if at least

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one of them is true, then the
orbital return are true. So true

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force gives me true. True force
gives me true true. True gives

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me 222 gives me true force and
force gives me a force force and

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force give me a force for so
true gives me a true and false

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or true. Me too again.

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And then the last step.

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Is that I need to use?

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The If then operation.

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Which two columns do I need to
use the Ethan operation for? I

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need to use for this?

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And I need to use for the
square bracket. Now this is

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my a because this is what on
the left side for the event

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symbol and this is my B
because this is on the right

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side of the if then symbol.

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True if then true returns a true

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value. Force even true returns a
true value true if then two

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returns at true Value Force if
then true returns with true

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value. True if then force
returns a force, why you force

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if then forced returns a true
value force if then true returns

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a true value, and force Tipton
true again returns 2 value.

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There is a curiosity about this
to table because if you look at

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the final output values, there
is only 1/4 output in here.

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Everything else is true.

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Let's finish this video with a
very complicated truth value

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table. Let me show you what you
have to do. If you have gold 4

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input values, so.

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PX or Q.

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And not R.

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If and only if.

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Not Q or S.

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Now I have got four different
letters PQ R&S not 2 to 4 =

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16. So I'm going to have a
rather long truth value table.

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So let's start building it up.
I've got P.

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I've got Q.

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I've got our.

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And I've got ***.

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Now what's the half of 16
half of 16 is 8, so I'm

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going to have to start with
putting down 8 truth.

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And eight forces.

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Just about then the
next step I'm going to

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put down four truths.

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N 4 forces.

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4 two again.

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And for force again.

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Next, 1/2 of four is 2, so
two through 2 fours.

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To to force force again until
I finish with the whole table.

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And in the last one is just 3/4,
alternating all the way down.

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OK, does this start up the
table? Then what I need to

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look at is breaking up the
brackets, finding out the

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priorities so there is a
square bracket and within the

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square bracket I have got a
normal bracket and are not so

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I can cut combine together PX
or Q.

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Then I would need to
find out the note R.

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In the five, being able to
calculate that, I will be

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able to calculate what is
inside the square bracket.

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Then once the square bracket has
been done, then I need to look

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at what's on the other side of
the if and only if symbol on the

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other side. I have got not Q or
S to be able to calculate that.

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First I need to calculate not Q.

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Then I can do the not Q or S.

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An once that's been done, I can
calculate the if and only if,

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which will give me the final
output. So let's get started PX

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or Q. What do I know about the X
or the X Rays, the xclusive, or

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which is only true if one or the
other is exclusively true? So

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basically, if the inputs are
different than the X, or will be

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true PX or Q?

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So the first 2 columns
they are the same, so the

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actual returns are force.

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They are different. The EXO
returns are true.

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They are different, so the
exhaust air returns are true.

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And in here they are the same,
so the X or returns are force.

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So the next column in R2 value
table will be the not R. So

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where are is true, North Star
will be force an when R is

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force, not R will be true.

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Force Force 3
Three Force Force

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3. Two force for street due
again, so I've got my starting

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values again. I need to
calculate what's inside the

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square bracket, so what's inside
the square bracket I'm combining

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together the X or and the North
R using the end operation.

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What do you remember about
the end operation? It's only

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true if both of them are
true, so let's came through.

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That is, both of them are true,
so I'm going to place a true

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sign there, same here.

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Here.

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Here.

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And the rest of them are all
different or double forces, so I

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can just fill in the last of the
table with force.

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Then calculate not Q while Q is
here and not Q will be just the

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opposite of what Cindy Q column
so true will be force.

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Annefors will be true.

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And then what I need to do here
is combined together, not Q.

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An S.

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Using the OR operation. So
what do I remember about the

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OR the OR is only force if
both of them are force? So

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let's try to filter out
those inputs, not both.

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Force both of them are
force, so this will be a

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force in here.

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Both of them are force,
so that's another force.

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Both of them are force.
Here is another force.

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Here is one more.

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So the rest of them I
can fill in with truth.

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Lovely, so the final answer is
the if and only if and what do I

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combine together to get the
final answer? On one side I've

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got the square bracket which is
here and the other side I have

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called the note Q or S which is
here. So if and only if returns

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true. If the inputs are the same
and it returns force if the

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inputs are different.

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To enforce difference, so the if
and only if gives me force force

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and force the same. So the if
and only if. It gives me true.

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Different force, same true,
different force, different

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force, same again true,
same different same.

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Same.

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Different gives me a force
different gives me a force

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different, gives me a force,
different, gives me a force and

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a different at the end. Again
gives me or force. So this is

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the final answer for this long
and rather complicated Boolean

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expression. And as you see there
are quite a bit of different

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combinations of force and truth.

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I hope that by now you have
been able to build a good

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understanding of the Boolean
expression and they threw

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tables. I have a few last
practice questions for you

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and the answers will follow,
so these are the practice

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questions.

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And here are the answers.