Pregunta
Question 3
a) Suppose
cat, dog, rabbit, mouse
dog, cow, duck, pig, rabbit
mouse, python
Find the following:
-
-
-
b) If
and
- Then find
,
- and also find
.
Question 4
By the use of a venn diagram, answer the following questions:
-
-
-
-
-
a) Suppose
mouse, python
Find the following:
b) If
Question 4
By the use of a venn diagram, answer the following questions:
Ask by Vega Davison. in South Africa
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Question 3
(a)
Given:
Given:
(b)
Given:
Given:
Question 4
In a Venn diagram:
-
includes all elements in or (or both). -
includes elements common to both and . -
(same as above). -
(same as ). -
includes elements not in or .
Solución
Question 3
(a)
We are given
We are given
-
To find
: -
First, compute
:
The common elements ofand are -
Now, take the union with
:
-
-
To find
: -
First, compute
: -
Now, intersect with
:
The elements ofare so we have
-
-
To find
: Assume that the complementis taken relative to the universal set -
We already found
-
Then the complement is
-
Now, intersect with
:
-
(b)
We are given
We are given
-
To find
: Sinceand are subsets of , we have Their union is -
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:
-
: This represents all elements that are in or in (or in both). In the Venn diagram, this is the entire area of both circles. -
: This represents the elements common to both and . In the Venn diagram, this is the overlapping region of the two circles. -
: (Same as above.) It is the overlapping region of and . -
: (Again, same as .) The intersection is commutative, so its representation is the same overlapping region. -
: 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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