Math Problem Statement
Solution
The question is asking which set of numbers represents those that are either less than or greater than or equal to .
Let's break down the options:
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: This set describes numbers that are either less than or greater than . This doesn't match the given condition fully, as it excludes numbers equal to .
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: This set describes numbers that are both less than and greater than , which is impossible, since a number cannot satisfy both conditions at the same time. So, this is incorrect.
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: This set describes numbers that are either less than or equal to or greater than or equal to . This seems like a valid match for the problem condition, which is looking for numbers less than or greater than or equal to .
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: This set describes numbers that are both less than or equal to and greater than or equal to , which is another impossible condition, because no number can satisfy both simultaneously.
Correct Answer:
The correct answer is , which matches the third option.
Would you like further details or have any questions?
Here are five related questions for further exploration:
- What is the difference between "and" and "or" in set notation?
- How do you represent inequalities on a number line?
- Can two inequalities combined with "and" ever result in an empty set?
- What is the union of two sets in terms of inequalities?
- How does set notation differ from interval notation?
Tip: Always pay close attention to the symbols used in inequalities, such as "or" (union) vs. "and" (intersection), as they drastically change the meaning of the solution set.
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Math Problem Analysis
Mathematical Concepts
Set Notation
Inequalities
Formulas
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Theorems
Union of Sets
Intersection of Sets
Suitable Grade Level
Grades 9-12