exercise9

# exercise9 - CSE541 EXERCISE 9 Problem 1 H is the following...

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 9 Problem 1 H is the following proof system: H = ( L {⇒} , F , AX = { A 1 ,A 2 } , MP ) A1 ( B ⇒ ( A ⇒ B )) , A2 (( B ⇒ ( A ⇒ C )) ⇒ (( B ⇒ A ) ⇒ ( B ⇒ C ))) , MP (Rule of inference) ( MP ) A ; ( A ⇒ B ) B (1) Prove that H is SOUND under classical semantics. (2) Does Deduction Theorem holds for H ? Justify. (3) Is H COMPLETE with respect to all classical semantics tautologies? Justify. Problem 2 Here are consecutive steps B 1 ,...,B 9 in a proof of (( B ⇒ A ) ⇒ ( ¬ A ⇒ ¬ B )) in H 2 of our Book. The comments included are incomplete. Complete the comments by writing all details. You have to write down the proper substitutions and for- mulas used at each step of the proof. B 1 = ( B ⇒ A ) Hypothesis B 2 = ( ¬¬ B ⇒ B ) Already proved formula: ( ¬¬ A ⇒ A ) for B 3 = ( ¬¬ B ⇒ A ) Already proved fact: ( A ⇒ B ) , ( B ⇒ C ) ‘ H 2 ( A ⇒ C ) B 4 = ( A ⇒ ¬¬ A ) 1 B 5 = ( ¬¬ B ⇒ ¬¬ A ) Already proved fact: ( A ⇒ B ) , (...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

exercise9 - CSE541 EXERCISE 9 Problem 1 H is the following...

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

View Full Document
Ask a homework question - tutors are online