Statistics - Intersection

 
   
     
       

Intersection

       

Understanding Intersection of Sets

       

          The intersection of two sets refers to the set of elements that are common to both sets. It is denoted by the symbol . If two sets have shared elements, their intersection forms a new set with just those common values.        

        Intersection A ∩ B      
     
       
         

Intersection Notation:

         
           

              \[               A \cap B = \{x \mid x \in A \text{ and } x \in B\}               \]            

         
         

This means the set of all elements x such that x is in both set A and set B.

         

Example:

         

Let:

         
           

              \[               A = \{2, 3, 4, 5\}, \quad B = \{3, 5, 7, 9\}               \]               \[               A \cap B = \{3, 5\}               \]            

         
         

Key Properties of Intersection:

         
               
  • Commutative: \( A \cap B = B \cap A \)
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  • Associative: \( (A \cap B) \cap C = A \cap (B \cap C) \)
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  • Idempotent: \( A \cap A = A \)
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  • Intersection with empty set: \( A \cap \emptyset = \emptyset \)
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Applications of Set Intersection:

         
               
  • Filtering common data from multiple lists or categories
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  • Used in database queries with common attributes
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  • In probability, finding overlap between events
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  • In Venn diagrams, showing shared characteristics
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