Math Problem Statement

n(AB)

Solution

To find the number of elements in the union of sets AA and BB, denoted as n(AB)n(A \cup B), we count all the unique elements within both sets AA and BB without double-counting those that appear in the intersection.

Elements in AA (from the diagram):

  • 9, 15, dd, bb, 5, cc

Elements in BB (from the diagram):

  • xx, 31, 12, ff, 5, cc

Union of AA and BB (combine all unique elements):

  • AB={9,15,d,b,5,c,x,31,12,f}A \cup B = \{9, 15, d, b, 5, c, x, 31, 12, f\}

Now, let's count these unique elements:

  • 9,15,d,b,5,c,x,31,12,f9, 15, d, b, 5, c, x, 31, 12, f

This gives us a total of 10 elements.

Thus, n(AB)=10n(A \cup B) = 10.

Would you like to explore anything else related to this problem?

Further Questions:

  1. What is n(AB)n(A \cap B), the number of elements in the intersection of AA and BB?
  2. How would you calculate n(A)n(A) and n(B)n(B) individually?
  3. What is the number of elements in the set difference ABA - B?
  4. What are the elements in the symmetric difference ABA \triangle B?
  5. How many elements are there in the universal set UU?

Tip: When working with unions and intersections, always pay attention to overlapping elements to avoid double-counting.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets
Intersection of Sets
Set Difference
Symmetric Difference
Universal Set

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12