Let's analyze and solve the problem shown in the image.

Problem Statement:

Given two sets:

• $R = \{2, 5, 6, 8\}$
• $T = \{6, 8, 9\}$

Find the following sets:

1. $\{ x \mid x \in R \text{ or } x \in T \}$
2. $R \cup T$

Solution:

1. Set Notation for $\{ x \mid x \in R \text{ or } x \in T \}$

This expression represents the union of sets $R$ and $T$, which means we need to include all elements that are in $R$ or in $T$.

$R \cup T = \{2, 5, 6, 8, 9\}$

So, $\{ x \mid x \in R \text{ or } x \in T \} = \{2, 5, 6, 8, 9\}$.

2. $R \cup T$

This is the same as the previous result because the union of two sets is represented by including all unique elements from both sets.

$R \cup T = \{2, 5, 6, 8, 9\}$

Final Answers:

(A) $\{ x \mid x \in R \text{ or } x \in T \} = \{2, 5, 6, 8, 9\}$

(B) $R \cup T = \{2, 5, 6, 8, 9\}$

It looks like you have selected the correct options for both parts in the image. Would you like further details or have any other questions?

Related Questions:

1. What is the intersection of sets $R$ and $T$?
2. What is the difference between sets $R$ and $T$?
3. How do you find the symmetric difference of two sets?
4. What are the basic operations that can be performed on sets?
5. How does the union operation differ from the intersection operation?

Tip: When performing set operations, always ensure to remove duplicate elements to maintain the properties of a set.