Final answer:
The union of sets A and B, A∪B, includes all integers less than or equal to 2 and all integers greater than or equal to 5.
Step-by-step explanation:
To find A∪B, which represents the union of set A and set B, we are looking for all elements that are either in set A or set B or in both. Given that A=z∈Z, this set includes all integers greater than or equal to 5. B=z∈Z, includes all integers less than or equal to 2.
When we combine these sets, the union will include all the integers from B which are up to 2, and all the integers from A starting from 5 and going upwards. There is no overlap between the two sets, as A contains only numbers 5 and above, and B contains only numbers 2 and below.
Therefore, the union A∪B will be {...,-2,-1,0,1,2,5,6,7,8,...}. Since we are dealing with the set of integers (Z), we will not list all of them but understand that it includes all integers less than or equal to 2 and all integers greater than or equal to 5.