Solutions17 - Chapter 17 Hints and Selected Solutions...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 17: Hints and Selected Solutions Section 17.1 (page 470) 17.1 Here for your convenience is the truth table ♣ ( P , Q , R ): P Q R ♣ ( P , Q , R ) t t t T t t f T t f t F t f f F f t t T f t f F f f t T f f f F This can be nicely captured as follows: ˆ h ( ♣ ( P , Q , R )) = ˆ h ( Q ) if ˆ h ( P ) = true ; ˆ h ( ♣ ( P , Q , R )) = ˆ h ( R ) if ˆ h ( P ) = false There are other ways of expressing the same thing, though. Just make sure that your definition gives the truth table above. 17.3 Assumethat h 1 and h 2 are truth assignments that assign the same value to the atomic sentences in S . We are asked to prove that ˆ h 1 ( S ) = ˆ h 2 ( S ). We prove this by induction on wffs. Basis: In this case S is itself atomic, so the assumption just immediately gives the result. Induction Step . There are several cases to consider, corresponding to the ways of building up propositional wffs. Here is one of the cases. Suppose that we know the result for P and Q and want to show that it is true for P ∨ Q . Our induction hypothesis insures us that ˆ h 1 ( P ) = ˆ h 2 ( P ) and ˆ h 1 ( Q ) = ˆ h 2 ( Q ). We know that ˆ h 1 ( P ∨ Q ) = true if and only if ˆ h 1 ( P ) = true or ˆ h 1 ( Q ) = true , or both, by the definition of...
View Full Document

This note was uploaded on 03/25/2009 for the course LOGIC 20034 taught by Professor Dhoe during the Spring '09 term at Hanover.

Page1 / 6

Solutions17 - Chapter 17 Hints and Selected Solutions...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online