Math Problem Statement

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Draw the Venn diagram of the following sets, where U is the universal set: U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {x | x ∈ ℤ and 0 ≤ x < 8}, and C = ∅.

Solution

The image contains a question about drawing a Venn diagram for the following sets:

  • U (Universal set) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
  • A = {1, 3, 5, 7, 9}
  • B = {x | x ∈ ℤ and 0 ≤ x < 8}, meaning B = {0, 1, 2, 3, 4, 5, 6, 7}
  • C = ∅ (empty set)

Steps for drawing the Venn diagram:

  1. Universal Set (U): Write all the elements of the universal set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} outside the circles.

  2. Set A: Circle A contains the elements A = {1, 3, 5, 7, 9}.

  3. Set B: Circle B contains the elements B = {0, 1, 2, 3, 4, 5, 6, 7}.

  4. Set C: Since C is the empty set, it will not contain any elements, and you do not need to draw anything for it.

Overlaps:

  • The intersection of sets A and B will include the elements they both share, which are {1, 3, 5, 7}.
  • Elements that are only in A but not in B are {9}.
  • Elements that are only in B but not in A are {0, 2, 4, 6}.

Venn Diagram Visualization:

  • Draw a rectangle representing U.
  • Inside the rectangle, draw two overlapping circles for A and B.
  • Place the elements in the correct sections based on the overlap and the elements in each set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Venn Diagrams
Set Operations

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9