Is My Solution to These Set Operations Correct?

In summary, the union of sets is an operation that combines all the elements from two or more sets into a single set. The intersection of sets is an operation that determines the common elements between two or more sets. A subset is a set that contains only a portion of the elements from another set, while a superset is a set that contains all the elements of another set and may have additional elements. The complement of a set is the set of all elements that are not present in the original set. Finally, a set can be both open and closed, known as a clopen set in topology.
  • #1
bergausstein
191
0
just want to make sure if my answer is correct

If $\displaystyle U\,=\,\{0,\,1,\,2,\,3,\,4,\,5,\,6,\,7,\,8,\,9\}$, the set of digits in our decimal system, and $\displaystyle A\,=\,\{0,\,1,\,2,\,3,\,4,\,5\}$, $\displaystyle B\,=\,\{2,\,3,\,4,\,5,\}$, $\displaystyle C\,=\,\{4,\,5,\,6,\,7\}$, $\displaystyle D\,=\,\{6,\,7,\,8,\,9\}$, find and tabulate:

a. $\displaystyle B'\,\cup\,D'$
b. $\displaystyle A'\,\cup\,B'$

here's my solution

$\displaystyle B'\,\cup\,D'\,=\,\{0,\,1,\,6,\,7,\,8,\,9\}\cup\{0,\,1,\,2,\,3,\,4,\,5,\}\,=\,U$
$\displaystyle A'\,\cap\,B'\,=\,\{6,\,7,\,8,\,9\}\cap\{0,\,1,\,6,\,7,\,8,\,9\}\,=\,\{\,6,\,7,\,8,\,9\}\,=\,D$
 
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  • #2
Re: Operations on set II

Looks good to me! (Sun)
 

FAQ: Is My Solution to These Set Operations Correct?

What is a union of sets?

The union of sets is an operation on two or more sets that combines all the elements from each set into a single set. The resulting set contains all the unique elements from each set. In set notation, the union of sets A and B would be written as A ∪ B.

How is the intersection of sets calculated?

The intersection of sets is an operation that determines the common elements between two or more sets. To calculate the intersection, we compare the elements of each set and include only the elements that are present in all sets. In set notation, the intersection of sets A and B would be written as A ∩ B.

What is the difference between a subset and a superset?

A subset is a set that contains only a portion of the elements from another set. In other words, all the elements of a subset are also present in the larger set. On the other hand, a superset is a set that contains all the elements of another set and may have additional elements that are not present in the smaller set.

How is the complement of a set determined?

The complement of a set is the set of all elements that are not present in the original set. It is denoted by Aᶜ, where A is the original set. To determine the complement, we first identify the universal set, which is the set of all possible elements. Then, we remove all the elements of the original set from the universal set to get the complement.

Can a set be both open and closed?

Yes, a set can be both open and closed. In topology, a set is considered open if it does not contain its boundary points, while a set is considered closed if it contains all its boundary points. Some sets, called clopen sets, satisfy both criteria and are therefore both open and closed.

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