Question: If R = {1, 4, 5, 6} and T = {4, 6, 7}, find the following sets. (A) {x | x ∈ R or x ∈ T} (B) R ∪ T…

If R = {1, 4, 5, 6} and T = {4, 6, 7}, find the following sets. (A) {x | x ∈ R or x ∈ T} (B) R ∪ T

(A) Select the correct choice below and fill in any answer boxes present in your choice.

A. {x | x ∈ R or x ∈ T} = {□} (Use a comma to separate answers as needed.) B. {x | x ∈ R or x ∈ T} is the empty set.

Solution

To solve the problem, we need to find the set \(\{x \mid x \in R \text{ or } x \in T\}\). Given: \(R = \{1, 4, 5, 6\}\) \(T = \{4, 6, 7\}\) The set \(\{x \mid x \in R \text{ or } x \in T\}\) is the union of the sets \(R\) and \(T\): \[ R \cup T = \{1, 4, 5, 6\} \cup \{4, 6, 7\} \] Performing the union operation, we combine all unique elements from both sets: \[ R \cup T = \{1, 4, 5, 6, 7\} \] So, the set \(\{x \mid x \in R \text{ or } x \in T\}\) is \(\{1, 4, 5, 6, 7\}\). The correct answer is option A: \(\{x \mid x \in R \text{ or } x \in T\} = \{1, 4, 5, 6, 7\}\).