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a.
To draw a Venn diagram for the true conditional statement and to determine the truth of the conclusion for a given statement.
a.
Answer to Problem 4PSA
True
Explanation of Solution
Given information: The true conditional statement is “If a person lives in Chicago, then the person lives in Illinois”.
The Given statement is true.
Given: Penny lives in Chicago.
Conclusion: Penny lives in Illinois.
A useful tool for determining whether or not a conditional statement is true or false is a Venn diagram.
The conclusion of above given statement is true.
As seen from Venn diagram, a person who lives in Chicago also lives in Illinois. Persons living in Chicago are subset of persons living in Illinois.
Conclusion:
The given statement is true.
b.
Illustrate the true conditional statement with Venn diagram and to determine the truth of the conclusion for a given statement.
b.
Answer to Problem 4PSA
False
Explanation of Solution
Given information: The true conditional statement is “If a person lives in Chicago, then the person lives in Illinois”.
The Given statement is true.
Given: Benny lives in Illinois.
Conclusion: Benny lives in Chicago.
A useful tool for determining whether or not a conditional statement is true or false is a Venn diagram.
The conclusion of above given statement is false.
As seen from Venn diagram, a person who lives in Illinois does not live in Chicago. Persons living in Illinois are not subset of person living in Chicago.
Conclusion:
The given statement is false.
c.
To show statement condition to be true with the help of Venn diagram and to determine the truth of the conclusion for a given statement.
c.
Answer to Problem 4PSA
False
Explanation of Solution
Given information: The true conditional statement is “If a person lives in Chicago, then the person lives in Illinois”.
The Given statement is true.
Given: Kenny does not live in Chicago.
Conclusion: Kenny must live in Illinois.
A useful tool for determining whether or not a conditional statement is true or false is a Venn diagram.
The conclusion of above given statement is false.
As seen from Venn diagram, a person who lives in Illinois must also live in Chicago.
Conclusion:
The given statement is false.
d.
To sketch a Venn diagram for the conditional statement which is true and to determine the truth of the conclusion for a given statement.
d.
Answer to Problem 4PSA
False
Explanation of Solution
Given information: The true conditional statement is “If a person lives in Chicago, then the person lives in Illinois”.
The Given statement is true.
Given: Denny does not live in Illinois.
Conclusion: Denny lives in Chicago.
A useful tool for determining whether or not a conditional statement is true or false is a Venn diagram.
The conclusion of above given statement is false.
As seen from Venn diagram, a person who does not live in Illinois will not live anywhere.
Conclusion:
The given statement is false.
Chapter 1 Solutions
Geometry For Enjoyment And Challenge
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