So it's 0, 0, 0, 0 please don't change it.

This is the language of sterility.

So what I want you to do is tell me for each of these sentences, whether it is valid, satisfiable but not valid, or unsatisfiable, in other words, false for all models.

And if you want to factor a p out of this, this is going to be equal to p times, if you take p divided p you get a 1, p square divided by p is p.

And the sentences are P or not P, P and not P,

And then this term over here, this whole thing over here, is going to be plus p times 1 is p. p times negative 2p is negative 2p squared.

Let's say that this is our grammar

It's actually a Bronze Age culture that's been isolated.

Once again, based on this P, I'm going to start bringing in rules 1 and 2.

F, L, E, P, T, P L, E, P, F, L, F, L, E, P, T, P, L, F, E, T.

APPLE.

Now in probability terms, people often write it as follows

The galaxy's a pretty barren, desolate place when you get right down to it.

Barren. Some even shattered.

You're stuck in the same deadend job. You have been for years.

Am i?

Let me just do this over here.

Redhead, redhead.

So chart state 0 includes the following parse states

Now let's add that pink p to both sides of this equation.

So that cancels out.

So this is going to be equal to 1 minus p.

Sterilization is not necessary.

Another way to think about that is let's say that we're in a particular state like this one

And I was inspired to study abroad after reading these.

I got a hair sample.

The first one looks pretty good. I just apply rule 1.

P of happiness given S and R times P of S and R, which is of course the product of those 2 because they are independent, plus P of happiness given not S R, probability of not as R plus P of H given S and not R times the probability of P of S and not R plus the last case,

P of A given B where B is the evidence and A is the variable we care about is P of B given A times P of A over P of B.

P

p.

What's next?

P .

P ... P ...?

Teacup!

Similarly, over here I'm going to apply rule one three times.

P...

Now divide both sides by 1 plus i.

P of X3 given X1 is the sum of P of X3 given X1 and A times P of A given X1 plus the A complement, which is X3, conditional X1 and not A times P of not A given X1.

Friends like Lual who died by my side, of starvation.

His legs. He's shaving his legs.

All right. E, F, L, E, P, T P, L, E, P, F, L, E L, E, P, T, L, P, E, F, E, T, Z, E, T...

It's that grammar of balanced parentheses.

Valid.

This is going to be, this term right over here is going to be p squared minus p to the third.