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Set Theory Concepts and Venn Diagrams

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Questions and Answers

What does the symbol '|' represent in the context of the solution?

The number of elements in a set (correct)

The union of two sets

The complement of a set

The intersection of two sets

What is the formula used to calculate the number of traders who sell both gari and rice?

$|P \cap Q| = |P| + |Q| - |P \cup Q|$

$|P \cup Q| = |P| + |Q| - |P \cap Q|$ (correct)

$|P \cap Q| = |P| + |Q| + |P \cup Q|$

$|P \cup Q| = |P| + |Q| + |P \cap Q|$

Why is it necessary to subtract the intersection of sets P and Q from the sum of their individual sizes when finding the number of traders selling both items?

To avoid counting traders who sell both items twice

Because traders who sell both items are included in both sets

To accurately represent the total number of traders

All of the above (correct)

What does the notation 'P \cap Q' represent in this context?

<p>Traders who sell both gari and rice (C)</p> Signup and view all the answers

What assumption is made about the traders in this problem?

<p>Each trader sells at least one of the two items (D)</p> Signup and view all the answers

Flashcards

Set Intersection

The set of elements common to both sets P and Q.

Set Union

The set of all elements in either set P or set Q.

Complement of a Set

Elements not in the specified set, denoted as Q'.

Number of Traders Selling Both

20 traders sell both gari and rice, denoted as |P ∩ Q|.

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Formula for Set Union

|P ∪ Q| = |P| + |Q| - |P ∩ Q|.

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Study Notes

Set Theory Concepts

Set P contains traders who sell gari.
Set Q contains traders who sell rice.
The total number of traders is 50.
30 traders sell gari, so |P| = 30
40 traders sell rice, so |Q| = 40
Each trader sells at least one item, meaning |P∪Q| = 50.

Venn Diagram Problem

The number of traders who sell both gari and rice (|P∩Q|) can be calculated using the principle of inclusion-exclusion.
|P∪Q| = |P| + |Q| - |P∩Q|
Substituting the given values, 50 = 30 + 40 - |P∩Q|
Solving for |P∩Q|, |P∩Q| = 20

Key takeaway

20 traders sell both gari and rice.

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Description

This quiz explores the concepts of set theory through a practical example involving traders selling gari and rice. You'll apply the principle of inclusion-exclusion to find the number of traders selling both items. Test your understanding of set operations and Venn diagrams.