Introduction to Logic

Deductions II

Deduce the conclusion of each of the following arguments from their premises (each answer given is a possible answer among many correct ones):

7)

1. ~ w . z
2. w v t t

8)

1. ~ a . b
2. a v c c . b

9)

1. a ~ b
2. b v c
3. a c

10)

1. x ~ y
2. y v w
3. x w v s

11)

1. x ~ y
2. ~ y t
3. x t . x

12)

1. p . q
2. p s
3. q r s . r

13)

1. p . r
2. (p v q) s s

14)

1. p . r
2. (p v q) s s . r

15)

1. p . r
2. (p v q) t
3. (r v w) s s . t

Answers

Question 7

7)

3. ~ w 1, Simp
4. t 2 , 3 D.S.

Question 8

8)

3. ~ a 1, Simp
4. c 2 , 3 D.S.
5. b 1, Simp
6. c . b
4, 5 Conj.

Question 9

9)

4. ~ b 1 , 3 M.P.
5. c 2 , 4 D.S.

Question 10

10)

4. ~ y 1 , 3 M.P.
5. w 2 , 4 D.S.
6. w v s 5, Add

Question 11

11)

4. ~ y 1 , 3 M.P.
5. t 2 , 4 M.P.
6. t . x 3 , 5 Conj.

Question 12

12)

4. p 1, Simp
5. s 1 , 4 M.P.
6. q 1, Simp
7. r
3 , 6 M.P.
8. s . r 5, 7 Conj.

Question 13

13)

3. p 1 , Simp
4. p v q 3, Add
5. s 2 , 4 M.P.

Question 14

14)

3. p 1, Simp
4. p v q 3, Ad

Question 15

15)

4. p 1, Simp
5. p v q 4 , Ad
6. t 2, 5 M.P.
7. r
7, Ad
8. r v w 3 , 8 M.P.
9. s 6 , 9 Conj
10. s . t