Question
The Venn diagram below shows the relationship among several sets of numbers.
Where should `-\sqrt{169}`be placed in the Venn diagram?
Where should `-\sqrt{169}`be placed in the Venn diagram?
Answers
GPT-4o mini
To find out where \(-\sqrt{169}\) should be placed in the Venn diagram, we first need to evaluate the expression.
Calculating \(-\sqrt{169}\):
\[
\sqrt{169} = 13
\]
Thus,
\[
-\sqrt{169} = -13
\]
Now, we need to determine the attributes of \(-13\) in relation to the sets in the Venn diagram. Here are some common sets to consider:
1. **Natural Numbers**: These are positive integers \(\{1, 2, 3, \ldots\}\). \(-13\) is not a natural number.
2. **Whole Numbers**: These are non-negative integers \(\{0, 1, 2, 3, \ldots\}\). \(-13\) is not a whole number.
3. **Integers**: These include all positive and negative whole numbers, as well as zero \(\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}\). \(-13\) is an integer.
4. **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers, including both integers and fractions. Since \(-13\) can be expressed as \(-13/1\), it is also a rational number.
5. **Real Numbers**: This set includes all rational and irrational numbers. Since \(-13\) is a rational number, it is also a real number.
Since \(-13\) does not belong to the sets of natural or whole numbers but does belong to the sets of integers, rational numbers, and real numbers, we can place \(-13\) in the intersection of the "Integers," "Rational Numbers," and "Real Numbers" in the Venn diagram.
To summarize, \(-\sqrt{169} = -13\) should be placed in the area representing integers, rational numbers, and real numbers, but outside the areas for natural numbers and whole numbers.
Calculating \(-\sqrt{169}\):
\[
\sqrt{169} = 13
\]
Thus,
\[
-\sqrt{169} = -13
\]
Now, we need to determine the attributes of \(-13\) in relation to the sets in the Venn diagram. Here are some common sets to consider:
1. **Natural Numbers**: These are positive integers \(\{1, 2, 3, \ldots\}\). \(-13\) is not a natural number.
2. **Whole Numbers**: These are non-negative integers \(\{0, 1, 2, 3, \ldots\}\). \(-13\) is not a whole number.
3. **Integers**: These include all positive and negative whole numbers, as well as zero \(\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}\). \(-13\) is an integer.
4. **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers, including both integers and fractions. Since \(-13\) can be expressed as \(-13/1\), it is also a rational number.
5. **Real Numbers**: This set includes all rational and irrational numbers. Since \(-13\) is a rational number, it is also a real number.
Since \(-13\) does not belong to the sets of natural or whole numbers but does belong to the sets of integers, rational numbers, and real numbers, we can place \(-13\) in the intersection of the "Integers," "Rational Numbers," and "Real Numbers" in the Venn diagram.
To summarize, \(-\sqrt{169} = -13\) should be placed in the area representing integers, rational numbers, and real numbers, but outside the areas for natural numbers and whole numbers.