Introduction to Logic

Deductions III

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

16)
1. (r . ~ p ) v ( r . q )
2. (p q) w w

17)

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

18)

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

19)

1. p v q p1
2. ~ ( p v r ) p2  
3. q w p3 w

20)

1. ~ ( p . q ) p1
2. ( p ~ q ) t p2
3. ~ t v w p3 w v z

21)

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

Answers

Question 16

16)

3. r. (~p v q) 1, Dist.
4. ~ p v q 3, Simp
5. p q
4, Imp
6. w 2, 5 M.P.

Question 17

17)

4. p ( t . s ) 1, Imp
5. (t . s) z 2, Imp
6. p z
4 , 5 H.S.
7. r 3 , 6 M.P.
8. r v w 7, Ad

Question 18

18)

4. r . (~ p v q) 1, Dist
5. ~ p v q 4, Simp
6. p q
5, Imp
7. w 2, 6 M.P.
8. t. s. 7, 3 D.S.
9. s 8, Simp

Question 19

19)

4. ~ p . ~ r 2, DeM
5. ~ p 4, Simp
6. q
1, 5 D.S.
7. w 6, 3 M.P.

Question 20

20)

4. ~ p v ~ q 1, DeM
5. p ~ q 4, Imp
6. t
5, 2 M.P.
7. w 6, 3 D.S.
8. w v z 7, Ad

Question 21

21)

4. t s 3, Imp
5. ( ~ p v ~ q ) t 2, Imp
6. r ( ~ p v ~ q )
1, DeM
7. r t 6, 5 H.S.
8. r s 4, 7 H.S.