Review for Test 3: MP, MT, CP, vI, DS, &I, &E, RA

Agenda

1. Office Hours: Monday after class Shatzle Hall Rm 314 (Seminar Room).
   Review Session: Wednesday at 4:30--You get it. 
2. Quiz
3. Questions about HW?
4. Mini Review of vI and DS
5. Practice for Test

Quiz
A.  Explain and give an example of the law of non-contradiction.
B.  Explain and give an example of the law of the excluded middle.
C. Translate:

1. If you're neither sure about how to do CP nor RA then you shouldn't go OUT and skip STUDYING.
2. You shouldn't watch CAT videos or and CUTE animal videos unless you've finished STUDYING. 

D. 

1. (Rv~S)>(T&~U)
2. (T&Q)>P        /:.  (P>~Q)>~(R&Q)

Translations

Mnemonics for conditional translations:
If P then Q; Q if P = P>Q. Rule: Whatever immediately follows the 'if' comes first.
P only if Q; Only if Q, P = ~Q>~P. Rule: Whatever follows 'only if' is negated then put first, the other proposition is negated and put after the '>'.
Unless P, Q; Q unless P = ~P>Q. Rule: Whatever follows 'unless' is negated and put first. Think of 'unless' as 'if not P'.
Other mnemonics:
Neither P nor Q= (~P&~Q)
P or Q but not both=(PvQ)&~(P&Q)

Practice
A. Unless you bring me either peanut butter COOKIES or DONUTS you won't get any BONUS points.
B. You can borrow the CAR only if you neither DRINK nor SMOKE.
C. Only if you start SQUATTING and DIETING now will you be ready for BEACH season.
D. If neither BOB nor GEORGE will help then I'll have to ask MARY or JERRY but I don't want to have to ask MARY.
E. If I survive the last WEEKS of this semester then I'm going to spend a week camping in the ROCKIES unless it RAINS or SNOWS.


Proofs: RA, CP, MP, MT, &I, &E, vI, DS, <>I, <>E
A.

1. /:. (P&~Q)>(Pv(S&T))

B. 

1. A
2. (~BvD)>F
3. ~(Dv~F)>~F
4. ~E>~C      /:.  (A>~B)>(C>~(D>~E))

C.

1. ~(Av~B)v(~CvD)
2. A&~D
3. ~(~C&A)vE    /:.  Ev(F>G)

D. 

1. /:.  (P>Q)<>(~Q>~P)

E*.  

1. /:.  ~(PvQ)<>(~P&~Q)

F. 

1. (RvP)>Q
2. (R>~S)>(Sv~Q)
3. ~P                        /:.  (R>~S)>~(RvP)

G. 

1. ~R
2. (~RvT)>(P>Q)    /:.  ~((P>Q)>~(~RvS))

H. 

1. ~(D&~B)v~A   /:.  A>(~B>(C>~(D&~B)))