Pregunta
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Question 3
a) Suppose cat, dog, rabbit, mouse dog, cow, duck, pig, rabbit
mouse, python
Find the following:

  1. b) If and
  2. Then find ,
  3. and also find .
    Question 4
    By the use of a venn diagram, answer the following questions:

Ask by Vega Davison. in South Africa
Mar 15,2025

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Question 3
(a)
Given:
(b)
Given:

Question 4
In a Venn diagram:
  1. includes all elements in or (or both).
  2. includes elements common to both and .
  3. (same as above).
  4. (same as ).
  5. includes elements not in or .

Solución

Question 3
(a)
We are given
  1. To find :
    • First, compute :
      The common elements of and are
    • Now, take the union with :
  2. To find :
    • First, compute :
    • Now, intersect with :
      The elements of are so we have
  3. To find :
    Assume that the complement is taken relative to the universal set
    • We already found
    • Then the complement is
    • Now, intersect with :
(b)
We are given
  1. To find :
    Since and are subsets of , we have
    Their union is
  2. To find :
    • First, find (elements in not in ):
    • The complement is taken relative to . Thus,

Question 4
In a Venn diagram the universal set is typically represented by a rectangle and the sets and by overlapping circles. The answers are as follows:
  1. : This represents all elements that are in or in (or in both). In the Venn diagram, this is the entire area of both circles.
  2. : This represents the elements common to both and . In the Venn diagram, this is the overlapping region of the two circles.
  3. : (Same as above.) It is the overlapping region of and .
  4. : (Again, same as .) The intersection is commutative, so its representation is the same overlapping region.
  5. : This represents the elements that are neither in nor in . In the Venn diagram, this is the area of the rectangle outside both circles.

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Beyond the Answer

When we dive into sets and Venn diagrams, we’re exploring the essence of relationships in mathematics! Sets are magical little collections that help us organize and understand data. For example, did you know that Venn diagrams were introduced by John Venn in 1880? They’re not just tools for math classes; they’re often used in logic, statistics, and even computer science!
Now, as you tackle these problems, remember common pitfalls: when computing intersections and unions, it’s easy to forget to meticulously list all elements without duplication. Always pay attention to the universal set context, especially when dealing with complements! To avoid confusion, draw your diagrams neatly, label them well, and keep track of your elements. Happy calculating!

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