
Concept explainers
(a)
To state:
Whether the given set is well defined.

Answer to Problem 1CR
Solution:
The given set is well defined.
Explanation of Solution
Given:
The given set is,
The set of all multiples of 5.
Definition:
A collection of objects is known as set. The objects in the set are known as elements.
Approach:
The set of all multiples of 5 is a well defined set. It always has same elements.
Thus, the given set is well defined.
Conclusion:
Therefore, the given set is well defined.
(b)
To state:
Whether the given set is well defined.

Answer to Problem 1CR
Solution:
The given set is not well defined.
Explanation of Solution
Given:
The given set is,
The set of difficult math problems.
Definition:
A collection of objects is known as set. The objects in the set are known as elements.
Approach:
The set of difficult math problems is not well defined. Different math problems will be difficult for different persons. For one problem some people would say it is not difficult and some people would say it is not.
Thus, the given set is not well defined.
Conclusion:
Therefore, the given set is not well defined.
(c)
To state:
Whether the given set is well defined.

Answer to Problem 1CR
Solution:
The given set is not well defined.
Explanation of Solution
Given:
The given set is,
The set of all great movies.
Definition:
A collection of objects is known as set. The objects in the set are known as elements.
Approach:
The set of all great movies is not well defined. For a same movie some people would say it is great movie and some people would say it is not.
Thus, the given set is not well defined.
Conclusion:
Therefore, the given set is not well defined.
(d)
To state:
Whether the given set is well defined.

Answer to Problem 1CR
Solution:
The given set is well defined.
Explanation of Solution
Given:
The given set is,
The set of all Oscar-winning movies.
Definition:
A collection of objects is known as set. The objects in the set are known as elements.
Approach:
The set of all Oscar-winning movies is a well defined set. It always has same elements.
Thus, the given set is well defined.
Conclusion:
Therefore, the given set is well defined.
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Chapter 2 Solutions
Mathematics: A Practical Odyssey
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