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Truth Tables and Natural Deduction (Make-Up Quiz Credit)

Name: Type Name Here

1 Truth Tables for Arguments (1.25 points each)

Use truth tables to determine if the arguments in 1-5 are either valid or invalid. Please use the inserted tables below to complete the truth tables. If the argument is invalid, please identify the row that violates the validity definition (e.g., “Invalid, 2nd row”).

(1) 1. A D

2. D A

3. D A

(2) 1. (F A) → A

2. A

3. (F A)

(3) 1. J (P J)

2. J

3. (J P)

(4) 1. (R K) (Q R)

2. Q Q

3. Q K

(5) 1. F (L Y)

2. ( L Y)

3. F

2 Natural Deduction Proofs (1.25 points each)

6-10 are each valid arguments. Demonstrate the validity of each argument using a natural deduction proof and MP, MT, DS, and HS inferences.

Copy and paste symbols into your proof where necessary:

∨ ∼

(6) 1. (Q ∼J) (M ∼D)

2. Q M

3. M ∼J / Q ∼D

(7) 1. (R L) (L ∼F)

2. ∼F ∨ (R L)

3. F / ∼R

(8) 1. C ∨ (H R)

2. S ∨ (R E)

3. ∼C

4. ∼S / H E

(9) 1. R ∨ B

2. (I H) ∼R

3. L (I T)

4. T H

5. L / B

(10) 1. (R F) [(R ∼G) (S Q)]

2. (Q F) (R Q)

3. ∼G F

4. Q ∼G / S F

Name:

Test 6B