1. The problem asks to find the intersection and union of given intervals using graphs. 2. Recall the definitions: - Intersection $A \cap B$ is the set of elements common to both $A$ and $B$. - Union $A \cup B$ is the set of elements in either $A$ or $B$ or both. 3. For the first pair: $[3, \infty)$ and $(6, \infty)$ - Intersection: Since $(6, \infty)$ starts at values greater than 6, the intersection is all numbers from just above 6 to infinity. - So, $$[3, \infty) \cap (6, \infty) = (6, \infty)$$ - Union: The union covers all numbers from 3 to infinity because $[3, \infty)$ already includes everything from 3 upwards. - So, $$[3, \infty) \cup (6, \infty) = [3, \infty)$$ 4. For the second pair: $[2, \infty)$ and $(4, \infty)$ - Intersection: Numbers greater than 4 are common to both intervals. - So, $$[2, \infty) \cap (4, \infty) = (4, \infty)$$ - Union: All numbers from 2 upwards are included. - So, $$[2, \infty) \cup (4, \infty) = [2, \infty)$$ Final answers: - $[3, \infty) \cap (6, \infty) = (6, \infty)$ - $[3, \infty) \cup (6, \infty) = [3, \infty)$ - $[2, \infty) \cap (4, \infty) = (4, \infty)$ - $[2, \infty) \cup (4, \infty) = [2, \infty)$