(5)With IP:
4. HAP/~H
5. AB1, 4 MP
97
EXERCISE 5-5:
(1) 4. PAP/~ (R M)
5. ~ P~ ~ Q1DeM
(3 ) 4. ~ [(EA)D]AP/ (E A)D
5. ~ (EA) ~ D4DeM
(5) 4. URAP/~(U R)
5. (R~S) (~ S R) 3 Equiv
(7 ) 4. AAP/B
5. ~ DC1,4 MP
98
(9) 4. GAP/ ~ G
5. HI2,4 MP
(11) 3. DAP/~B
(13) 4. BAP/~B
5. DE2,4 MP
(15) 4. NTAP/M
5. N4Simp
99
EXERCISE 5-6:
(1) 1. AAP/A B
(3 ) 1. AAP/~A B
2. AB1Add
(5) 1. ABAP/C(A B)
10
(7 ) 1. A B AP/ (A B) (B A)
2. AAP/B A
3. A~B2Add
(9) 1. ABAP/ ~ B~A
2. ~ BAP/~A
EXERCISE 5-7:
(1) 4. ~ C~D1,3 MP
5. ~ (CD) 4 DeM
10
(5) 4. ~ ~ A~C2DeM
5. ~ ~ A4Simp
(7) 5. K2,4 DS
(9) 7. A~A6Add
8. ~ D3,7 MP
EXERCISE 5-8:
1 is valid. 3 and 5 are invalid.
EXERCISE 5-9:
10
(1) 3. AAP/C
(3) 2. ABAP/ ~ (A B)
3. ~ A1E
(5) 2. ABAP/ ~ (A B)
3. A2E
(7) 2. BAP/A
3. ~ AAP/~ ~ A
(9) 2. ~ (BA)AP/ ~ ~ (B A)
3. BAP/~B
10
(11) 2. AAP/ (B C)
3. BAP/C
(15) 2. ~ [(AB) (~ A~B)] AP/ ~ ~ [(A B) (~ A~B)]
3. AAP/~A
10
EXERCISE 6-1:
(1) 1. p q p
(3) 1. (p q)rp
(5) 1. ~ p~qp
10
(7) 1. ~ (p~q) p
2. rpp/ r q
(9) 1. p q p/ ~ q p
(11) 1. p q p
(13) 1. p q p
10
(15) 1. p(p p) p
2. q(p q) p
(17) 1. ~ (p~q) p
2. r p p/ r s
(19) 1. p q p
10
EXERCISE 6-2:
(1) 1. p q
2. p~q
(3) 1. p q
(5) 1. p q
(7) 1. p q
10
(9) 1. ~ (p q)