Consider the set A = {1,2,7,8). The partially ordered set (P(A), C) is the power set of A with elements partially ordered by inclusion. This means that given X,Y ? P(A), if X ? Y, then X is less than or equal to Y, and Y is greater than or equal to X in the given partial ordering.
Which of the following sets are less than or equal to {1,2} in the inclusion ordering on P(A)?
? {1,8}
? {2,8}
? ?
? {7}
? {1,2,7,8}
? {8}
? {1,2,8}
? {2,7,8}
? {1}
? {1,7,8}
? {7,8}
? {1,2}
? {2}
? {2,7}
? {1,2,7}
? {1,7}
Which of the following sets are greater than or equal to {1,2} in the inclusion ordering on P(A)?
? {1}
? {1,2}
? {1,8}
? {7}
? {1,2,7}
? {7,8}
? {1,7}
? {2,7,8}
? {2}
? {2,7}
? {2,8}
? ?
? {8}
? {1,2,7,8}
? {1,2,8}
? {1,7,8}
