Construct a formal proof in proving the following argument. Follow the steps presented in this section. Use the given variables for its simple components. If I work, then I earn money, but if I am idle, then I enjoy myself. Either I work or I am idle. However, if I work, then I do not enjoy myself, while, I am idle then I do not earn money. Therefore, I enjoy myself if and only if I do not earn money. (w, m, i, e)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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Create the argument form either horizontally or vertically
9:10 PM | 0.0KB/s & 9
ll all ? E
Stepl
a)
Given the variables,
w: work,
m: money
I: idle
e: enjoy
Step2
b)
In the proof above, the terminologies we have used are
v: Disjunction
A: Conjunction
→: Implication
+: Double implication
- : Negation
If I work, then I earn money: w → m.
If I am idle, then I enjoy myself: i → e.
Either I work or I am idle: w V i.
If I work, then I do not enjoy myself: w → ~e.
While I am idle, then I do not earn money:
i → -m.
I enjoy myself if and only if I do not earn
money: e +→ ~m.
VX
Transcribed Image Text:9:10 PM | 0.0KB/s & 9 ll all ? E Stepl a) Given the variables, w: work, m: money I: idle e: enjoy Step2 b) In the proof above, the terminologies we have used are v: Disjunction A: Conjunction →: Implication +: Double implication - : Negation If I work, then I earn money: w → m. If I am idle, then I enjoy myself: i → e. Either I work or I am idle: w V i. If I work, then I do not enjoy myself: w → ~e. While I am idle, then I do not earn money: i → -m. I enjoy myself if and only if I do not earn money: e +→ ~m. VX
2. Construct a formal proof in proving the following argument. Follow the steps presented in
this section. Use the given variables for its simple components.
If I work, thenlearn money, but if I am idle, then I enjoy myself. Either I work or I
am idle. However, if I work, then I do not enjoy myself, while, I am idle then I do
not earn money. Therefore, I enjoy myself if and only if I do not earn money. (w,
m, i, e)
Transcribed Image Text:2. Construct a formal proof in proving the following argument. Follow the steps presented in this section. Use the given variables for its simple components. If I work, thenlearn money, but if I am idle, then I enjoy myself. Either I work or I am idle. However, if I work, then I do not enjoy myself, while, I am idle then I do not earn money. Therefore, I enjoy myself if and only if I do not earn money. (w, m, i, e)
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