Question

Consider the set n of positive integers to be the universal set. sets​ h, t,​ e, and p are defined to the right. determine whether or not the sets upper e prime font size decreased by 10 and upper p prime are disjoint. h equals startset n is an element of upper n vertical line n greater than 100 endset t equals startset n is an element of upper n vertical line n less than 900 endset e equals startset n is an element of upper n vertical line n is even endset p equals startset n is an element of upper n vertical line n is prime endset

Answer 1

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.

$\text{Universal Set}, U=\{n|n \in \mathbb{Z}^+\}, where \mathbb{Z}^+ is the set of positive integers.$

$H=\{n|n \in \mathbb{N}| n>100\}\\T=\{n|n \in \mathbb{N}| n$

We are to determine if the sets E' and P' are disjoint.

E' and P' are the complements of E and P respectively.

Therefore:

$E'=\{n|n \in \mathbb{N}| n is odd \}\\P'=\{n|n \in \mathbb{N}| n is not prime\}$

The intersection

$E' \cap P' =\{n|n \in \mathbb{N}| n is odd but not prime \}$

Therefore, the sets E' and P' are not disjoint.