Math Problem Statement
Which of the following are true and which are false? (a) 10 ∈/ (−∞, π2 ). (b) π ∈ (2, ∞).
Solution
Let's break down each statement:
Statement (a)
- The notation means that 10 is not an element of the interval .
- The interval represents all real numbers less than (about 1.57).
- Since 10 is clearly greater than , it does not belong to this interval.
So, Statement (a) is true. .
Statement (b)
- The notation means that is an element of the interval .
- The interval represents all real numbers greater than 2.
- Since , which is indeed greater than 2, it belongs to this interval.
So, Statement (b) is true. .
Final Answer:
- (a) True
- (b) True
Would you like more details on these statements, or do you have any questions about intervals or set notation?
Related Questions:
- What is the meaning of and in set theory?
- How do open and closed intervals differ, and what does that affect?
- Can you explain the difference between intervals like and ?
- How do you convert radians to degrees, and vice versa, when working with intervals?
- What is the significance of in mathematics and its approximations?
Tip: Always remember that means numbers less than , and means numbers greater than . If you're unsure, just think of the number line!
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Math Problem Analysis
Mathematical Concepts
Set Theory
Intervals
Real Numbers
Formulas
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Theorems
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Suitable Grade Level
Grades 9-11
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