(b) (My program runs successfully) or (the system bombs and I blow
my stack). Furthermore, (the system does not bomb) or (I don’t
blow my stack and my program runs successfully). Therefore, my
program runs successfully.
Solu tion
(a) IBM: IBM will take over the copier market
Xerox: Xerox will take over the copier market
RCA: RCA returns to the computer market
( )
(
( )
1
2
¬
∨
→
∴ ¬
IBM Xerox)
RCA IBM
RCA
Proof:
1.
¬
∨
(IBM xerox)
P
2.
RCA IBM
→
P
3.
¬
∧ ¬
IBM
xerox
(1), De Mor gan’s Law
4.
¬ IBM
(3), Sim pli fi ca tion
5.
¬ RCA
(2), (4), Modus Tollens
(b) S: My program runs successfully
B: System bombs
BS: I blow my stack
¬ ∨ ¬
∧
∨ ∧
∴
B
BS S
S B BS
S
(
)
(
)
(To prove)
Proof:
1.
S B BS
∨ ∧
(
)
P
2.
¬ ∨ ¬
∧
B
BS S
(
)
P
3.
(
) (
)
S B
S BS
∨ ∧ ∨
Distributivity of (1)
4.
(
) (
)
¬ ∨ ¬
∧ ¬ ∨
B
BS
B S
Distributivity of (2)
5.
S B
∨
(3), Sim pli fi ca tion
6.
¬ ∨
B S
(4), Sim pli fi ca tion
7.
S
B
∨ ¬
(6)
8.
(
) (
)
S B
S
B
∨ ∧ ∨ ¬
(5), (7), Conj.
9.
S B
B
∨ ∧ ¬
(
)
10. S ∨ 0
11. S
Hence proved.
Prop o si tions and Pred i cates
273