Problem 1.1. Let A = {{},d, (a,c).b} (a) What is | A|? (b) Which of the following are elements of A: a, b, c, {d), (a,e), (a,c), b). ., (o). {{})? (c) Which of the following are subsets of A: a, b, e, (d), (a,e), {{a,c}, b), es. (or). {{}}? (d) Can A be the power set of some set? (e) Write down a partition of A. Problem 1.2. Let A be as above, and let B = {{1} , (0} , b,e}. What is (a) AnB? (b) AAB? (c) (1 ) in A AB? (d) (A x B) \\ { (x,y) E A x B| x = (0} ory = (0}}? Problem 1.3. Let X and Y be sets. Prove that XAY = (XUY) \\ (XnY) using a Venn diagram