Respuesta :
Given:
Universal set is all positive integers {1,2,3...}
Set A is the set of all positive ODD integers {1,3,5,7...}
The question asks us to find [tex]A^{c}[/tex], which is the complement of set A. The complement of a set refers to elements NOT in that set. Hence, complement of A should be all the elements NOT in A but in Universal Set, U.
It is clear from the question that set A houses all the odd positive numbers, so complement of A will have all the even positive numbers. Last choice is the correct one.
ANSWER: [tex]A^{c} =[/tex] "{x|x ∈ U and is an even positive integer}"
You can use the definition of complement of a set to find out the value of [tex]A^c[/tex]
The set that describes [tex]A^c[/tex] is given by:
Option D: [tex]A^c[/tex] = {x|x ∈ U and is an even positive integer}
What is a complement of a set?
Firstly there is universal set specified in a given context which contains all the set discussed there in that context if not otherwise restricted. It is generally indicated by U.
Let there is a set A in this universal set. Then its complement set would contain those elements of U which are not in U.
The complement of a set is written as [tex]A^c[/tex]
How to find the complement of set A here?
Since U is set of all positive integers, and A contains all odd positive integers, and since if an integer is not odd, it is surely even, thus the complement of A would contain all positive even integers since only those positive even integers are not in A which are in U.
Thus, we have
Option D: [tex]A^c[/tex] = {x|x ∈ U and is an even positive integer} as correct choice.
Learn more about complement of set here:
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