Respuesta :
Answer:
The sets E' and P' are not disjoint.
Step-by-step explanation:
Definition: Two sets are disjoint if their intersection is an empty set.
The sets are defined as follows.
[tex]\text{Universal Set}, U=\{n|n \in \mathbb{Z}^+\},$ where \mathbb{Z}^+$ is the set of positive integers.[/tex]
[tex]H=\{n|n \in \mathbb{N}| n>100\}\\T=\{n|n \in \mathbb{N}| n<900\}\\E=\{n|n \in \mathbb{N}| n$ is even$\}\\P=\{n|n \in \mathbb{N}| n$ is prime\}[/tex]
We are to determine if the sets E' and P' are disjoint.
E' and P' are the complements of E and P respectively.
Therefore:
[tex]E'=\{n|n \in \mathbb{N}| n$ is odd$\}\\P'=\{n|n \in \mathbb{N}| n$ is not prime\}[/tex]
The intersection
[tex]E' \cap P' =\{n|n \in \mathbb{N}| n$ is odd but not prime$\}[/tex]
Therefore, the sets E' and P' are not disjoint.
