Final answer:
The correct answer True. The statement 2∈A is True as the number 2 is a member of set A which is {2, 4, 5, 6, 7, 8}. The intersection and union of sets A and B are {6, 7} and {1, 2, 4, 5, 6, 7, 8} respectively, correcting any misconceptions regarding set operations.
Step-by-step explanation:
The statement 2∈A is asking whether the number 2 is an element of set A. Given that set A is defined as {2, 4, 5, 6, 7, 8}, it is clear that the number 2 is indeed a member of set A. Therefore, the statement 2∈A is True.
When determining the intersection (AND) and the union (OR) of two sets, the intersection represents all elements that are common to both sets, while the union represents all elements that are in either set. If we apply this to sets A and B, the intersection A AND B would be {6, 7}, and the union A OR B would be {1, 2, 4, 5, 6, 7, 8}.
It is also important to correct any false statements with accurate set operations. For instance, the claim that A AND B = {14, 16, 18} is incorrect since none of these numbers are in both A and B. Similarly, asserting A OR B = {2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19} includes elements not present in either A or B and thus is incorrect.