This is what B3 looks like :

6. Come up with any POSET that is a Boolean algebra isomorphic to B3. Represent the relation using either a matrix or by listing the ordered pairs. Hint, pick any 8-element set and use your image of B3 to form the relationships. 111 110 101 011 100 010 001 000 7. If (A,R) is a POSET where A = {1,2,3,4,5}, is it possible for (A,R) to represent a Boolean algebra? Answer 'Yes', 'No', or 'There is not enough information' and justify your answer. 8. If (A,R) is a POSET where A = {1, 2, 3, 4, 5, 6, 7, 8}, is it possible for (A,R) to represent a Boolean algebra? Answer 'Yes', 'No', or 'There is not enough information' and justify your