Homework Part 1. Due next Tuesday, 2/19/19 Recall the definitions of reflexive, symmetric and transitive relations. Recall, too, that a relation is a set of ordered pairs. Section 2.5.2 in Makinson (p44) defines the following: A similarity relation is when a relation is both reflexive and symmetric, but not transitive. An equivalence relation is when a relation has three properties - transitivity, symmetry and reflexivity. Unfortunately, Makinson does not define a relation type when a relation is reflexive and transitive, but not symmetric. I will call this an "aintbad" relation because, "Two out of three ain't bad." (1) Using the 2/12 lab as a starting point, create three functions: similarity? equivalence? aintbad? that will test a binary relation "R" over A, where A = {1, 2, 3} to see if it qualifies as one of these relations. (2) Find a test case that will work for each one of the above three functions. You can have as many tester test cases (that fail any/all three functions) as you like, but you should have one test case that will pass one of the functions above for a total of three. WHAT TO HAND IN: No need to email a program to me. Print off your definitions file and a copy of your interactions file and hand them both in before Tuesday's lecture. A RUBRIC OF SORTS: Total of 10 points. 2 points each for finding a test case that works and includes failing test cases. (6) 2 points for properly commenting code (2) 2 points for properly formatting code (2) -2 points if you omit your name.