Modus Tollens and Conjunction Rules

Class
1. Review:

• Validity
• Translation
• Modus tollens (MT)

2. Conjunction Rules (&In and &Out)
3. Bonus Office Hours This Week: 4:20pm 3rd Floor Shatzel Hall, Seminar Room

Conjunction Rules: &In and &Out

A.  &In

1. P
2. Q
3. P&Q

B.  &Out

1. P&Q
2. P/Q

Proofs with DN and MP Only

A.

1. ~~(P>~~~Q)>~~~~S
2. S>~~(Q>P)
3. P>~~~Q
4. (Q>P)>~~~T
5. ~T>Q  /:. ~~Q

Proofs 

MT Only

B. 

1. ~A>(B>C)
2. ~(B>C)
3. A>~B  /:. ~B

C. 

1. ~S>(Q>~R)
2. P
3. (Q>~R)>~P  /:. S

MP, MT, DN

D. 

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

E. 

1. T>U
2. ~(~P>~Q)>(~R>~S)
3. (~R>~S)>~(T>U)
4. ~P   /:.  ~Q

F. 

1. ~Q>T
2. P
3. ~(P>~Q)>(~R>T)
4. ~(~R>T)
5. S>~T  /:. ~S

MP, MT, DN, &In, &Out

H. 

1. ~E>~A
2. A>B
3. (A>B)>(A>~(D&E)
4. A>D
5. A