OK.
So let's look at some truth tables the way you set up a truth table is if P and Q And let's say we have
two variables we're 0 0 1 1 0 1 0 1.
That's all the options that we could have as far as things go.
If the 0 0 option is 0 1 option the 1 0 option the 1 1 option if you just say p and q we would do 0
0 0 0 1 0 1 0 0 1 and 1 is 1.
If it is a not p and q we would not.
This column would be 1 1 1 0 and if it is a P X or not p and q then we take this p and q x word with
P and we'll see that 1 and 0 is 1 0 and 1 is 1 1 and X soared with 1 is 0 and 1 x or with 0 is 1.
So if we took that Pinti X or did when I was saying and but we're exploring it with an upping you that's
what we get.
Now that's for two variables.
If we wanted to try something with three variables let's say we had p q in our So we have to have all
the possibilities.
There's going to be eight different possibilities of what could happen there.
So this is how we do what we do forand more than two and two and then one in one.
Those are the different possibilities of everything that could happen as far as P-Q an hour ago.
Now if I said something like you know then you can just follow the same logic for your truth table and
get some type of output.
For instance you could have p and q or R and then you do p and q or R is zero p and q or R is 1 p and
q or R is zero p and q or R is one exception and you can keep going with that and do that.
If you had four variables you'd have to have 16 options and then do that whole thing.
But at the end of the day it's really just a matter of breaking down the logic step by step and then
seeing what it is.
So if you were to have something like p and q and we'll say and R and let's put this in brackets and
we will X or this with P or not Q Then what do you do you set up your table.
You do it step by step P or Q Then you do it and with the R.
Then you do this side P or not.
Q And you x4 those two.
You can name this a and you can name is B and you could X for those two and that's how you go about
doing it step by step with the truth table seeing what it is just following it.
Now I want to note that P or Q In terms of Maff if we have.
Ones and zeros if we just have different options like this.
It's not exactly a plus but it's the idea that an OR is similar to a plus because that would be as if
this is not exactly a plus but it's similar to a plus.
So we'd be bat so we could designate or as saying P plus Q.
It's just that it's only that would be the only difference.
And we could do the same thing with the and.
And we can designate the Nannes to be similar to multiplication where we would say something like 0
0 0 0 1 that's the same as multiplication p and q is the same as p times Q That 0 0 0 and that's a 1.
So that's something that we'll use later and one and one.
One plus one you might say oh that's two but it's really just means that it went through just like a
circuit diagram where it could go either way.
It could go on the top or it could go on the bottom.
It doesn't matter one and one would just be that it went through with Doesn't matter which circuit it
went through.
So that's how we think about it.
With pluses and multiplication.
So instead of using these Amzah honors we could use multiplication and addition.