Relations. Closures of Relations Objectives: Introduce relations and their properties. Examples of relations in mathematics. Representation of relations by direct graphs. Closures of relations. Instruction: 1. Write about relations, their properties, and operations on them. Give a few examples illustrating your text. Explain how to direct graphs could be used to represent relations. Describe closures of relations. Transitive closures. 2. Chose one of the problem sets below. Solve the problems, provided clear explanation of each step. 3. Upload your file into this assignment. Problem Set I Pg. 581-582 (Rosen text): # 4(a, b), 6(a, e), 12 and 18, 34. Pg. 606-607: #2, 5, 16(b), 18(b) Problem Set II Pg. 581-582 (Rosen text) # 4(a, c), 6(f, g), 12 and 18, 36. Pg. 606-607: #3, 6, 16(c), 18(c) Problem Set III Pg. 581-582 (Rosen text) # 4(a, d), 6(b, f), 12 and 18, 40. Pg. 606-607: #2, 7, 16(d), 18(d)