Introduction to Logic

Deductions 1

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

1)

1. ~p . r
2. p v q q

2)

1. ~p . r
2. p v q q . r

3)

1. p ~ q
2. q v r  
3. p r

4)

1. p ~ q
2. q v r
3. p r v w

5)

1. w . r
2. w s  
3. r t s . t

6)

1. w . r
2. w s
3. r t
4. (s . t) z z

 

Answers

Question 1

1)

3. ~p 1, Sim
4. q 2 , 3 D.S.

Question 2

2)

3. ~ p 1, Sim
4. q 2 , 3 D.S.
5. r 1, Simp
6. q . r 4, 5 Conj.

Question 3

3)

4. ~ q 1 , 3 M.P.
5. r 2 , 4 D.S.

Question 4

4)

4. ~q 1 , 3 M.P.
5. r 2, 4 D.S.
6. r v w 5, Ad.

Question 5

5)

4. w 1, Simp
5. r 1, Simp
6. s 2 , 4 M.P.
7. t
5 , 3 M.P.
8. s . t 6, 7 Conj.

Question 6

6)

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