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[Music] hi im adam this is the machine tech video blog and today im going to continue our discussion on auto collimators in the previous video i described in a very general sense how auto collimators work including why they are only sensitive to angular changes in a mirror and why thats so useful i also casually mentioned that based on the focal length of the objective lens in the auto collimator as well as on the resolution of the scale and the magnification of the eyepiece both of which have to do with sensing the movement of the return image of the crosshair you can tell exactly what the angular change of that mirror is very very precisely in this video were going to explore those relationships further which means were going to have to dig even deeper into optics and the related math but dont worry im going to try to cover this as intuitively as i possibly can and luckily all of the parameters i just described are related through a very simple formula the autocollimator form

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How do you calculate DNF and CNF?

Simply write down the truth table, which is quite simple to find, and deduce your CNF and DNF. If you want to find DNF, you have to look at all rows that ends with T. When you find those rows, take the x,y, and z values from each respective column. Thus, you get (xyz)(xyz)(xyz)(xyz).

What is the difference between DNF and CNF?

CNF is an of s, where is over variables or their negations (literals); an of literals is also called a clause. DNF is an of s; an of literals is called a term.

What is resolution in predicate logic?

Resolution is an inference rule that produces a new clause. from two clauses with complementary literals (p and p).

What is resolution rule in logic?

The resolution inference rule takes two premises in the form of clauses ( The two premises are said to be resolved and the variable x is said to be resolved away. Resolving the two clauses x and x gives the empty clause.

What is CNF vs DNF?

CNF is an of s, where is over variables or their negations (literals); an of literals is also called a clause. DNF is an of s; an of literals is called a term.

Can a DNF be a CNF?

Yes, the formula AC can both be interpreted as CNF and DNF.

What is the resolution method?

Resolution method is an inference rule which is used in both Propositional as well as First-order Predicate Logic in different ways. This method is basically used for proving the satisfiability of a sentence. In resolution method, we use Proof by Refutation technique to prove the given statement.

What is CNF used for?

Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. Each clause connected by a conjunction, or AND, must be either a literal or contain a disjunction, or OR operator. CNF is useful for automated theorem proving.

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