hw1-sol

# hw1-sol - CSE596 Fall 2011 Solution to Homework 1 A formula...

This preview shows pages 1–2. Sign up to view the full content.

CSE596 Fall 2011: Solution to Homework 1 September 20, 2011 1. A formula F is a tautology every assignment to its variables satisﬁes it no assignment to its variables satisfy ¬ F ⇔ ¬ F is not satisﬁable 2. First of all, note that every variable (or its negation) is in conjunctive normal form. Assume that A = A 1 A 2 ∧ ··· ∧ A k and B = B 1 B 2 ∧ ··· B l are formulas that are already in conjunctive normal form. We need to show that A B , ¬ A and A B can be expressed in conjunctive normal form (CNF from now on). Since A B is equivalent to ¬ ( ¬ A ∧¬ B ), it suﬃces to show the above for A B and ¬ A . Clearly, A B = A 1 A 2 ∧···∧ A k B 1 B 2 ∧··· B l is already in CNF. In order to convert ¬ A ≡ ¬ A 1 ∨¬ A 2 ∨···¬ A k A 0 1 A 0 2 ∨···∨ A 0 k (where A 0 i is a conjunction, by applying De Morgan’s law to the clause A i ) to CNF, we observe the distributive law : ( a b ) c ( a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw1-sol - CSE596 Fall 2011 Solution to Homework 1 A formula...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online