H and F are sets of real numbers defined as F={zlz>4} H={zlz<=9} what would be the Fnh and Fuh?

Question

what would be the F∩H and F∪H in interval notation?

Answer 1

Think of the intersection (∩) of two sets just like the intersection of two roads: It's what they share in common. So, F∩H is the real numbers the two sets share. Set F is all numbers greater than 4 but less than or equal to 9. That can be expressed as 4<z≤9, but the question specifies "interval notation." In interval notation that would be (4,9].

 

The union (υ) of sets is analogous to joining the two. So FυH is, in this case, all real numbers because when you combine all the numbers greater than 4, which is the set F, with all of the numbers less than or equal to 9, you get all of the real numbers. In interval notation that is (-∞,∞).