exercise11sol

# exercise11sol - CSE541 EXERCISE 11 SOLUTIONS 12 Read and...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: CSE541 EXERCISE 11 SOLUTIONS Chapters 10, 11, 12 Read and learn all examples and exercises in the chapters as well! QUESTION 1 Use the (complete) proof system GL from chapter 11 to prove that | = ( ¬ ( a ∩ ¬ b ) ⇒ ( ¬ a ∪ b )) . Solution By completeness theorem for GL we have that | = A is and only if ‘ GL-→ A . We construct a decomposition tree for our formula as follows. T → A-→ ( ¬ ( a ∩ ¬ b ) ⇒ ( ¬ a ∪ b )) | ( →⇒ ) ¬ ( a ∩ ¬ b )-→ ( ¬ a ∪ b ) | ( → ∪ ) ¬ ( a ∩ ¬ b )-→ ¬ a,b | ( → ¬ ) a, ¬ ( a ∩ ¬ b )-→ b | ( ¬ → ) a-→ ( a ∩ ¬ b ) ,b ^ ( → ∩ ) a-→ a,b axiom a-→ ¬ b,b | ( → ¬ ) a,b-→ b axiom All leaves are axioms, hence the tree is a proof of A in GL . QUESTION 2 Find a counter-model determined by a decomposition tree T → A in GL for a formula A below. A = (( a ∩ ¬ b ) ⇒ ( ¬ a ∪ b )) 1 Solution: We construct a decomposition tree for → A formula as follows....
View Full Document

## This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.

### Page1 / 3

exercise11sol - CSE541 EXERCISE 11 SOLUTIONS 12 Read and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online