**Consider the Statement:** "Only a rich man can own a home in Palatine." a) **Put this statement in the if ... then format:** If someone owns a home in Palatine, then they are a rich man. b) **Indicate the negation of this statement in English:** There exists a person who is not a rich man and owns a home in Palatine. c) **Indicate the contrapositive of this statement in English:** If someone is not a rich man, then they cannot own a home in Palatine. d) **With respect to the properties "Being rich" and "Owning a home in Palatine", according to this statement which one is sufficient for the other and which one is necessary for the other?** - Being rich is necessary to own a home in Palatine. - Owning a home in Palatine is sufficient to conclude that someone is rich.
**Consider the Statement:** "Only a rich man can own a home in Palatine." a) **Put this statement in the if ... then format:** If someone owns a home in Palatine, then they are a rich man. b) **Indicate the negation of this statement in English:** There exists a person who is not a rich man and owns a home in Palatine. c) **Indicate the contrapositive of this statement in English:** If someone is not a rich man, then they cannot own a home in Palatine. d) **With respect to the properties "Being rich" and "Owning a home in Palatine", according to this statement which one is sufficient for the other and which one is necessary for the other?** - Being rich is necessary to own a home in Palatine. - Owning a home in Palatine is sufficient to conclude that someone is rich.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Consider the Statement:**
"Only a rich man can own a home in Palatine."
a) **Put this statement in the if ... then format:**
If someone owns a home in Palatine, then they are a rich man.
b) **Indicate the negation of this statement in English:**
There exists a person who is not a rich man and owns a home in Palatine.
c) **Indicate the contrapositive of this statement in English:**
If someone is not a rich man, then they cannot own a home in Palatine.
d) **With respect to the properties "Being rich" and "Owning a home in Palatine", according to this statement which one is sufficient for the other and which one is necessary for the other?**
- Being rich is necessary to own a home in Palatine.
- Owning a home in Palatine is sufficient to conclude that someone is rich.
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