11. Create a set A of names of people that you know. (Limit |A| to a max of 15). Define some relation (write it down and explain what the relation is) that will map a few of the people in set A to other people in set A. (Your relation could be something like: "they are in the same family", or "they play golf together", or whatever). As you did in problem #10, create a Word table to represent A x A. Again, highlight aRa in yellow on the chart Highlight the identity relation in red, and also on the chart.

A={1,2,3,4,5,6} and consider the following 3 subsets of A. A = {1,3,5}; A2 = Let {2, 4, 6}; A3 = {3, 6}.

Problem 7. Which of the following relations ~on Z is an equivalence relation? Explain your answer, and for each relation that is an equivalence relation, give the set Z/~ of all equivalence classes. 1

Let A,B,C be sets with A = 50, |B| = 99, and C = 142. Draw a Venn Diagram to represent each of the following restrictions, and determine |AU BUC. (a) ACBCC. (b) The sets are pairwise disjoint (Read the second help link if you do not know what this means). (c) Sets A and B have 8 common elements, sets A and C have 11 common elements, sets B and C have 28 common elements, and there are 3 elements common to all three sets.

9.12. Let S = {a, b, c}. Then R = {(a, a), (a, b), (a, c)} is a relation on S. Which of the properties reflexive, symmetric and transitive does the relation R possess? Justify your answers.