Is 9 an element of {1,4,5,8}∩{5,8,9}{1,4,5,8}∩{5,8,9}?    Is  {(1,2),(2,2)}{(1,2),(2,2)} a subset of the set {0,2}×{1,2}{0,2}×{1,2}?

To determine if 9 is an element of {1,4,5,8}∩{5,8,9}, we first need to find the intersection of the two sets {1,4,5,8} and {5,8,9}. The intersection of two sets is a set that contains all elements that are common to both sets. In this case, the intersection is {5,8}. Since 9 is not in this set, 9 is not an element of {1,4,5,8}∩{5,8,9}.

To determine if {(1,2),(2,2)} is a subset of the set {0,2}×{1,2}, we first need to understand what the Cartesian product of two sets is. The Cartesian product of two sets A and B, denoted by A×B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In this case, {0,2}×{1,2} = {(0,1), (0,2), (2,1), (2,2)}. The set {(1,2),(2,2)} is not a subset of {0,2}×{1,2} because the pair (1,2) is not in the Cartesian product set.