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Logical and Numerical Reasoning
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Patterns, Connections, and Inductive Reasoning
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Unit Analysis and Scientific Notation
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Sets and Venn Diagrams
The Venn diagram below can be used to model the relationships among three categories of fruit.
Set A:Fruits that are red (e.g., apples, red peppers,...)
Set B: Fruits that are sweet (e.g., oranges, strawberries...)
Set C: Fruits that are roundish (e.g., grapes, apples, ...)
Overlapping regions (sets) show fruits that belong to multiple categories. For example, a red, sweet, and round fruit like a red apple would be in the intersection of all three sets, which is Region (or set) G.
a. What category of fruit would you find in region E? Give an example.
b. A fruit in Region H would be sweet and roundish, but not red. True or false?
c. If we consider bananas to be sweet, in what region or regions would you find them?
d. A fruit in Region E would be red and roundish, but not sweet. True or false?
e. Name a fruit in Region G.
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Suppose you want to classify the numbers from \(1\) to \(20\) into three categories: Even numbers, Prime numbers, and Multiples of \(5\). Here are the three sets of numbers:
Set A Even numbers from 1 to 20:\(\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}\)
Set B Prime numbers from 1 to 20: \(\{2, 3, 5, 7, 11, 13, 17, 19\}\)
Set C Multiples of 5:\(\{5, 10, 15, 20\}\)
Create a Venn diagram to show the relationships between these sets.