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.