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Questions and Answers
What does the symbol '|' represent in the context of the solution?
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?
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?
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?
What does the notation 'P \cap Q' represent in this context?
What assumption is made about the traders in this problem?
What assumption is made about the traders in this problem?
Flashcards
Set Intersection
Set Intersection
The set of elements common to both sets P and Q.
Set Union
Set Union
The set of all elements in either set P or set Q.
Complement of a Set
Complement of a Set
Elements not in the specified set, denoted as Q'.
Number of Traders Selling Both
Number of Traders Selling Both
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Formula for Set Union
Formula for Set Union
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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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