ICS-241 M. Bauer Homework for Exam 03 Given the relation on {1,2,3,4} represented by the following zero-one matrix: 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1) Is it reflexive? _______ If not, what ordered pairs must be added to make it reflexive? 2) Is it symmetric? ______ If not, what ordered pairs must be added to make it symmetric? 3) Is it antisymmetric? _______ If not, explain the minimum removals necessary to make it antisymmetric? Given the relation on {1,2,3,4} represented by the following directed graph: 1 2 3 4 4) Is it reflexive? _______ If not, what ordered pairs must be added to make it reflexive? 5) Is it symmetric? ______ If not, what ordered pairs must be added to make it symmetric? 6) Is it antisymmetric? _______ If not, explain the minimum removals necessary to make it antisymmetric? Given the relation on {1,2,3,4} represented by {(1,1), (1,3),(1,4), (2,1), (2,2), (3,1), (3,2), (3,3) (4,1), (4,4)} 7.) Is it reflexive? _______ If not, what ordered pairs must be added to make it reflexive? 8) Is it symmetric? ______ If not, what ordered pairs must be added to make it symmetric? 9) Is it antisymmetric? _______ If not, explain the minimum removals necessary to make it antisymmetric? 10.) 1 1 0 1 Find M2 for the relation on {1,2,3,4} represented by following zero-one matrix: 1 0 0 1 0 0 1 1 0 0 1 1 11.) 0 1 0 1 Find M2 for the relation on {1,2,3,4} represented by following zero-one matrix: 1 1 0 0 0 1 1 1 1 1 0 1 12.) Given M* for a relation on {1,2,3,4} is represented below, express the transitive closure as a set of ordered pairs. 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 13.) Given M* for a relation on {1,2,3,4,5} is represented below, express the transitive closure as a set of ordered pairs. 1 0 0 0 [0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1] 14.) Create a zero-one matrix representation of a relation on {1,2,3,4} which is symmetric. 15.) Create a zero-one matrix representation of a relation on {1,2,3,4} which is antisymmetric. 16.) Create a set of ordered pairs representation of a relation on {1,2,3,4} which is an equivalence relation, other than the one given in question 20. 17.) Create a set of ordered pairs representation of a relation on {1,2,3,4} which is a partial order. 18.) Create a zero-one matrix representation of a relation on {1,2,3,4,5} which is an equivalence relation, other than the one given in question 20. 19.) Create a zero-one matrix representation of a relation on {1,2,3,4,5} which is a partial order. 20.) What are the equivalence classes of the following equivalence relation {(1,1), (1,4), (2,2), (3,3), (3,5), (4,1), (4,4), (5,3), (5,5), (6,6)}?