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.