Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer: Choice D) set of even integers
=======================================================
Explanation:
U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}
A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}
[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}
[tex]A^c[/tex] = {set of even numbers from set U}
In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]
The opposite of the odd numbers is the set of even numbers.
Therefore, we go for choice D as our final answer.
Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.