c. Lefty: Muscles was shooting craps with Socko when Sharky was knocked off. d. Muscles: Lefty didn't kill Sharky. Who did kill Sharky? In 41-44 a set of premises and a conclusion are given. Use the valid argument forms listed in Table 2.3.1 to deduce the conclusion from the premises, giving a reason for each step as in Example 2.3.8. Assume all variables are statement variables. 42. a. p V q b. 9→r с. p^s→t d. ~r е. ~q→u^s f. .'. t 43. а. ~p →r^~s

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Chapter2: Second-order Linear Odes
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Discrete math. I'm stuck on Q42, and another image is an example of the solution.

2.4
APPLICA
c. Lefty: Muscles was shooting craps with Socko
when Sharky was knocked off.
d. Muscles: Lefty didn't kill Sharky.
Who did kill Sharky?
42. а.
p V q
9→r
p^s →t
d.
с.
~r
In 41-44 a set of premises and a conclusion are given. Use
the valid argument forms listed in Table 2.3.1 to deduce the
conclusion from the premises, giving a reason for each step as
in Example 2.3.8. Assume all variables are statement variables.
е.
f. .. t
~q→u ^ s
43. а.
~p→r^~s
Transcribed Image Text:2.4 APPLICA c. Lefty: Muscles was shooting craps with Socko when Sharky was knocked off. d. Muscles: Lefty didn't kill Sharky. Who did kill Sharky? 42. а. p V q 9→r p^s →t d. с. ~r In 41-44 a set of premises and a conclusion are given. Use the valid argument forms listed in Table 2.3.1 to deduce the conclusion from the premises, giving a reason for each step as in Example 2.3.8. Assume all variables are statement variables. е. f. .. t ~q→u ^ s 43. а. ~p→r^~s
1.
RK → GK
by (a)
GK → SB
by (b)
.. RK → SB
by transitivity
2.
RK → SB
by the conclusion of (1)
~SB
by (c)
.'. ~RK
by modus tollens
3.
RL V RK
by (d)
~RK
by the conclusion of (2)
... RL
by elimination
4.
RL → GC
by (e)
RL
by the conclusion of (3)
.'. GC
by modus ponens
Thus the glasses are on the coffee table.
Transcribed Image Text:1. RK → GK by (a) GK → SB by (b) .. RK → SB by transitivity 2. RK → SB by the conclusion of (1) ~SB by (c) .'. ~RK by modus tollens 3. RL V RK by (d) ~RK by the conclusion of (2) ... RL by elimination 4. RL → GC by (e) RL by the conclusion of (3) .'. GC by modus ponens Thus the glasses are on the coffee table.
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