Logic Homework for Monday 3/13

I. Use the short method to check the validity of the arguments in 6.9 #1, 2, 5, 6, 9, 10, 11.

II. Use the following rules to do Natural Deductions:

Modus Ponens Modus Tollens Hypothetical Syllogism

A → B A → B A → B

A ~ B B → C

\ B \ ~ A \ A → C

Disjunctive Syllogism Conjunction Simplification

A v B A A & B

~ A B \ A

\ B \ A & B

Identify the rule used in the following 1-step arguments:

1. (D v E) & (F v G) 2. (S → T) v [(U & V) v (U & V)] 3. (F v G) → ~ (G & ~ F)

\ D v E ~ (S → T) ~ (G & ~ F) → (G → F)

\ (U & V) v (U & V) \ (F v G) → (G → F)

4. (A → B) → (C v D) 5. N → (O v P) 6. (C v D) → [(J v K) → ~ E]

(A → B) Q → (O v R) ~ [(J v K) → ~ E]

\ (C v D) \ [N → (O v P)] & [Q → (O v R)] \ ~ (C v D)

Identify the line numbers and rules used to justify each step in the following deductions:

(7) 1.(E v F) & (G v H) (8) 1. I → J

2. (E → G) & (F → H) 2. J → K

3. ~ G 3. ~ L

\ H 4. I v L

4. E v F \ K

5. G v H 5. I → K

6. H 6. I

7. K