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

video we will look at some
more examples of relatively

simple trick tables.

Now let's look at an
example, which is a slightly

bit more difficult, not.

P or Q.

And are so in this case now I
have got three different inputs

because I have got three
different letters, so the number

of rows in my throught table
which is calculated by two to

the N. In this case an the
number of inputs is 3, therefore

this will be two to three, which
is 8. So I have got P.

I have got Q and I have caught
R and the input combination half

of eight is 4, so I'm going to
copy four trues an I'm going to

copy for forces.

Then I'm just going to copy
two truths, two forces

until I finish filling the
table, and then in the last

column I'm just going to do
them, alternating 1 by 1.

Now, in this case you can see
that I have got every different

combinations and I'm not
repeating any one of them, so

this is the starting of the
setup of the table. Now what are

the intermediate steps before we
can actually find the final

answer for the output? Now there
is a bracket and within the

bracket I have got P or QP or Q
will have to be one. I need to

calculate. But then there is
a node operation in front, so

I going to have to apply that
to the output of P or Q and

then at the end I'm going to
have to use.

The end operation to combine
everything together so P or Q,

I'm going to use this table. Now
what do I know about the OR

the OR only returns force if
both of the inputs are force? So

I'm going to run through the
table and find the only inputs

when both of them are force.

And the rest of them I can just
quickly fill in.

By truth, I could have gone
through two or two, gives me

through three or two, gives me
through, etc. But this one is a

nice and easy shortcut to

remember. What does the note do?

Change three to force and change
forced to true so the top half

up to here is true. So every one
of them will be force.

And the bottom two forces which
get then will turn into truth.

And then I have to do the final
combination of not P or Q&R. So

which are the two that I need to
combine together? Here I need to

use this input.

And I need to use the R.

And what do I know about the end
and is only true if both of them

are true? So I'm going to go
through the Roseanne. I'm going

to filter out. Do I have double
trues in here? I have one in

here. And I haven't got it
anywhere else, so the rest of

them will have to be filled in
with forces becausw.

And it's only true if both of
the inputs are true. In any

other cases, the end will be
force, so knowing this shortcuts

can save you quite some time on
filling in the tables.

And now let's look at the last
example for this video.

P. If only if.

Q and not R. So this is
a similar example to the

previous one because PQ&R I've
again have got three different

inputs, so P.

Q.

R.

Due to the power three gives
me 8, so it's to start the

through table of correctly.
I'm going to have to place

than four truth four forces.

Two truth 246.

And then just alternating
them 1 by 1.

Right set up starting, setup,
done correctly. Then what do I

need to look at? I need to look
at my priorities.

There is a bracket here and
inside the bracket that is Q and

not R to be able to combine
together Q and not our first I

need to know what the values are
for not R so that's what I need

to calculate first. Once I've
got the values for not RI can

calculate Q and not R.

And once that's done, I can
combine P together with the Q

and not R using the if and
only if operation.

Let's get started. R is
here, So what is not R every

true becomes false an every
force becomes true.

So now which are the two columns
that I need to combine together

to find Q and not RI need Q?

And I need not R.

So and operation the end only
returns true if both of the

inputs are true. So I'm going to
try to filter those ones out.

And the rest of them I'm going
to fill in with force. Now, if

you are not using lined paper,
then you want to be very careful

about making sure that you
lining these trees and force

values relatively easy to see,
because if you are getting a

little bit wonky then you might
take a force for the upper or

lower row instead of the road
that it belongs to. So be

careful with that. Now I've got
Q and not R.

But what I need here now is the
if and only if table.

Remember if and only if it's
true. If the two input values

are exactly the same and it's
false if the input values are

different. So which columns am
I going to use here? But I

need to use P.

And I need to use the Q and not
R, which we just calculated

here. So if they are the same,
I'm going to return true. If

they are the different, I'm
going to return force. So look

at this through force different.
So I'm returning a force true

through the same. I'm returning
a true true enforce different.

I'm returning a horse through
unforced, different returning or

force force and force the same.

I'm returning a tree 4th century
different. I'm returning a

force. Force and force the
same. I'm returning a true and

force on force the same.
Again, I'm returning the true.

I hope you are gaining
confidence in finding solutions

to trig tables now in the next
couple of videos we will look at

some more difficult examples.
However, now it's your turn to

do some practice questions. The
answers are at the end.

So these are the practice
questions.

And here are the answers.