Problem 4: Let A be the set of 3-bit binary strings: A={000, 001, 010, 011, 100, 101, 110, 111}. Treat O as equivalent to False (F), and l as equivalent to True (T). Let o be the bit-wise logical and operation between the elements of A. For example, 101 O 011 = 001. Define the following relation R in A: x Ry if x o y = x (where x,y e A). a) Prove that R is a partial order. b) Is R a total order? c) Draw the graph of R and the Hess diagram of R. d) Does A have a maximum? If so, what is it? 1 e) Does A have a minimum? If so, what is it? f) Let B= {001, 010, 011, 110}. If B has a maximum, give its maximum; otherwise, give the maximals of B. Also, if B has a minimum, give its minimum; otherwise, give the minimals of B