HOMEWORK #5

Propositional Logic III

Last Update: 18 February 2005

Note: or material is highlighted

Prove that the following rules of inference are derivable from our rules of ¬Intro, ¬Elim, ^Intro, ^Elim, vIntro, vElim, Intro, and Elim:
1. Modus Tollens (or "Denying the Consequent"; a variety of Elim; also, a variety of ¬Intro):
```
	From (  )
	and ¬
	--------------
	Infer ¬
	
```
2. Hypothetical Syllogism (or "Transitivity of the Material Conditional"; a variety of Intro)
```
	From (  )
	and (  )
        --------------
	Infer (  )
	
```
3. Constructive Dilemma (or "Reasoning by Cases"; a variety of vIntro):
```
	From ( v )
	and (  )
	and (  )
        --------------
	Infer ( v )
	
```
Represent the English sentences from HW #3, problem #3, in our language for propositional logic in such a way that you can prove that sentence 3e follows validly from sentences 3a-3d. Then prove it syntactically!

DUE: AT THE BEGINNING OF LECTURE, FRIDAY, FEB. 25