Question
If the set U = {all positive integers} and set A = {x|x ∈ U and x is an odd positive integer}, which describes the complement of set A, Ac?
Ac = {x|x ∈ U and is a negative integer}
Ac = {x|x ∈ U and is zero}
Ac = {x|x ∈ U and is not an integer}
Ac = {x|x ∈ U and is an even positive integer}
Ac = {x|x ∈ U and is a negative integer}
Ac = {x|x ∈ U and is zero}
Ac = {x|x ∈ U and is not an integer}
Ac = {x|x ∈ U and is an even positive integer}
Answers
GPT-4o mini
To determine the complement of the set A, denoted as Ac, we need to understand what the set A consists of and then identify the elements that are not in this set.
The set A is defined as follows:
\[ A = \{ x | x \in U \text{ and } x \text{ is an odd positive integer} \} \]
This means A contains all positive odd integers, such as 1, 3, 5, 7, and so on.
The universal set U consists of all positive integers:
\[ U = \{ 1, 2, 3, 4, 5, \ldots \} \]
The complement of set A, Ac, will include all positive integers that are **not** in A. Since A contains all odd positive integers, Ac will include all positive integers that are not odd, which are the even positive integers.
Therefore, the correct description of Ac is:
\[ Ac = \{ x | x \in U \text{ and is an even positive integer} \} \]
Hence, the correct answer is:
**Ac = {x|x ∈ U and is an even positive integer}**.
The set A is defined as follows:
\[ A = \{ x | x \in U \text{ and } x \text{ is an odd positive integer} \} \]
This means A contains all positive odd integers, such as 1, 3, 5, 7, and so on.
The universal set U consists of all positive integers:
\[ U = \{ 1, 2, 3, 4, 5, \ldots \} \]
The complement of set A, Ac, will include all positive integers that are **not** in A. Since A contains all odd positive integers, Ac will include all positive integers that are not odd, which are the even positive integers.
Therefore, the correct description of Ac is:
\[ Ac = \{ x | x \in U \text{ and is an even positive integer} \} \]
Hence, the correct answer is:
**Ac = {x|x ∈ U and is an even positive integer}**.