Where clauses aren't required.

So immediately we have two clauses.

Eight negative clauses are hidden in this composition.

Then the actions have two new types of clauses.

They are words that connect clauses, words, and phrases.

That's going to total up to n clauses in the formula.

They are words that connect two unequal things, dependent and independent clauses.

Adverbial time clauses (here 'when') write about the future in the present tense.

That basically means slash is valid and then any number of these clauses is valid after that.

The way it knows that there are new clauses forming right here is this colon right over here.

There's no other clauses that we need to consider here that captures the notion of k color ability.

In list comprehensions we can also put little clauses or guards to only take some of the input list.

This formula that we come to has k variables and s clauses and we're going to add three more nodes.

Then we have some additional clauses that say what can't be the case that a is red and b is red at the same time.

Remember all the clauses end up being in these groups, so there's one clause for each node that says that that node has to have one of the k colors.

So we create one of these gadgets for each for each in the clauses connect them to the rest of the graph and now we get this giant graph and that whole graph is satisfied, if and only all the gadgets can be colored, which is the same as saying if and only all the clauses can be satisfied and since they're all connected with n, that's exactly what we wanted it to be.

I want to know how many clauses are in the formula, and just to make that a bit more concrete a clause is the sort of thing that I got here in parenthesis, it's between the n's.

So imagine we've got 3 colors, 8 nodes and 20 edges, how many clauses are in the formula that result from converting this 3 colorability problem into a satisfiability problem, and when you have your answer, write it in this box and we'll check it for you.

Basically, it has to start with and then it contains one or more of the following characters little a through little z, big A through big Z, 0 through 9, underscore, and dash followed by an optional slash and then as many of those clauses as you want.

It's just that form that I showed you before where the formula is the n of a bunch of clauses and each clause is the or of three literals and each literal is either variable or its negation, not the variable, so you walk up to me with 3 CNF problem,