Math

QuestionExplain well-defined vs. not well-defined sets. Which statement is true? A, B, C, or D? Which sets are well-defined? A, B, C, D, E?

Studdy Solution

STEP 1

Assumptions1. A well-defined set is one where it is clear whether any given object belongs to the set or not. . A set that is not well-defined is one where it is not clear whether any given object belongs to the set or not.

STEP 2

From the given options, the correct definition of a well-defined set is option A "A set is well-defined if any given object can be classified as belonging to the set or not belonging to the set."
Correct Definition A\text{Correct Definition A}

STEP 3

Now, let's identify which of the given examples are well-defined sets.

STEP 4

Option A "The set of all students enrolled in school" is a well-defined set. We can clearly determine if a person is a student enrolled in a school or not.
Well-defined Set A\text{Well-defined Set A}

STEP 5

Option B "The set of all people who are tall" is not a well-defined set. The term "tall" is subjective and can vary from person to person.
Not Well-defined Set B\text{Not Well-defined Set B}

STEP 6

Option C "The set of all United States presidents" is a well-defined set. We can clearly determine if a person has been a president of the United States or not.
Well-defined Set C\text{Well-defined Set C}

STEP 7

Option D "The set of all integers that are not1 or2" is a well-defined set. We can clearly determine if a number is an integer that is not1 or2.
Well-defined Set D\text{Well-defined Set D}

STEP 8

Option "The set of all dogs that are large" is not a well-defined set. The term "large" is subjective and can vary from person to person.
Not Well-defined Set\text{Not Well-defined Set}So, the well-defined sets are A, C, and D while the sets that are not well-defined are B and.

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